Three of the world's most influential women have told BBC News they want to end child marriage within a generation.

Michelle Obama, Amal Clooney and Melinda French Gates announced last year a collaboration between their foundations to combat the problem.

At the current rate of progress, the UN has warned it will not be eradicated for 300 years.

But former First Lady Mrs Obama told BBC News: "It is an issue that can be solved tomorrow."

The three women spoke exclusively to BBC 100 Women during a visit to Malawi and South Africa.

"I'm sorry," said 26-year-old Lucy, as she choked back tears. "I feel emotional."

Lucy was in the library of Ludzi Girls secondary school in the central region of Malawi. US secret service agents stood outside, under the red flame trees of the school grounds. She had just been speaking about the importance of girls staying in school, and spared the fate of marriage to much older men, before emotion suddenly overcame her.

Around the table, three of the world's most influential humanitarians - Melinda French Gates, Amal Clooney and Michelle Obama - had quietly listened to her story.

According to the NGO, Girls Not Brides, Malawi has one of the highest child marriage rates in Eastern and Southern Africa, with 42% of girls already married by the age of 18. In Mchinji District, where Ludzi Girls school is located, 33% of girls are reported to fall pregnant before they reach 18, and leave education.

Lucy could have been one of those girls. Her father had wanted her out of school when she was 14, but she resisted, and later became the first girl in her village to go to university. Now, with a degree in education, she is a district leader for AGE Africa, an organisation that provides scholarships for vulnerable girls in Malawi, a country where secondary education is not free. Lucy was once a student in the programme, and now she helps girls like herself.

Her mother is overjoyed at her achievement, Lucy said, although her father is less so. She said he is still coming to terms with an independent daughter. Sharing all this left her overwhelmed.

The former First Lady of the US, sitting to Lucy's left, spoke up. "Will you send your father a message for me? Next time you see him, tell him that Michelle and Barack Obama are so proud of you, and the woman you have become."

Lucy looked up, smiling. On Lucy's right sat international human rights barrister Mrs Clooney. "And tell him you have a lawyer too now," she added.

Mrs Obama's education-focused organisation, Girls Opportunity Alliance, had already identified that girls around the world were leaving school due to pregnancy and teenage marriage. Mrs Clooney was working to make sure girls in rural communities were aware of their rights, and many of Ms French Gates's projects had focussed on improving healthcare - including treatment for girls who experience complications after giving birth at a young age.

All are passionate about defending the rights of women and girls, so a coalition seemed like a natural fit.

"It's been a really lovely and very organic partnership, and friendship, between the three of us," international human rights lawyer Mrs Clooney told BBC 100 Women.

"In an early conversation with the Gates Foundation, I said: 'You're working on gender justice at a massive scale, but mostly you're not using law as a tool. You're looking at economics, and you're looking at health. Maybe we can form a partnership?'"

Ms French Gates, who got a spontaneous cheer from the Ludzi schoolgirls when she said it was her fifth visit to Malawi, said working together was a strategic decision, and that their overlapping areas of expertise would make them more effective.

"Women, I think, naturally work in collectives," she told the BBC. "I've talked to a number of women who are older than me who made it as CEO, or CFO, in their company. And there's some regret that they didn't do it in concert with other women. They didn't pull other women up and along with them. The generation that we've been part of - Michelle and I are essentially the same age - we've wanted to pull everybody up with us."

According to Unicef, 650 million girls and women are alive today who married under the age of 18, and currently more than 12 million girls a year marry in legal and traditional ceremonies around the world. South Asia and Sub-Saharan Africa have the highest rates globally, but this is not just an issue in the global south. Five states in the US have no minimum age of marriage as long as parents consent.

Some countries, such as Malawi, have progressive laws that outlaw marriage under the age of 18, although these often come up against longstanding cultural barriers. On Monday, following the visit of the three campaigners, President Lazarus Chakwera announced further funding for a national strategy to end child marriage. Until now there have been very few prosecutions.

Mrs Clooney thinks outreach is a solution. Her Waging Justice for Women programme funds the Women Lawyers Association of Malawi, which arranges for specialists to travel to rural communities to seek out women looking for help. More than 85% of Malawi's population lives in villages, set in expanses of land governed by chiefs, living in huts under baobab trees, miles from roads and electricity.

"We formed a network of mobile legal aid clinics, which means literally, there's a van that goes out with lawyers, and we go out in a community and say to girls, 'These are your rights. If you need a lawyer - for free - to protect you, we are here.

"We wage justice, and we say 'waging' because you can't assume it's going to happen," Mrs Clooney said. "You have to form alliances and fight against these kinds of injustices with the determination that it takes to win a war."

The BBC visited a legal clinic under a makeshift tent in a village in Mchinji district - it had more than 1,000 attendees, mostly women. Some were pregnant teenagers, asking what they could do to stay in school after giving birth.

"I see myself in the girls that we're fighting for," Mrs Obama told the BBC. "I see my daughters in those girls."

There is, however, concern this issue has no solution, at least in the short term. In a report earlier this year, Unicef said child marriages now made up 19% of all marriages, down from 23% 10 years ago. But it added that eliminating child marriage could still take about 300 years.

"This is an urgent issue," said Mrs Obama. "We can't afford to ignore it and assume that we can make headway on all the other big stuff that we're trying to deal with - poverty, climate change, war, and the rest - unless we're doing right by 50% of our population.

"It is an issue that can be solved tomorrow. If all the world leaders got together and made it a priority, it wouldn't take 300 years. It could happen in less than a generation."

Michelle Obama, Amal Clooney and Melinda French Gates chose to visit Malawi because each of their programmes was already supporting projects in the country. What form their long-term collaboration will take is still being worked out, but for now the women say they will back in-country organisations that have been working with communities for years.

"Large scale international organisations that are supposed to be dealing with this, like the UN Security Council, like powerful governments, are not delivering," said Mrs Clooney. "So I think philanthropy and individuals have to play a larger role."