How common was it for underage men (15-17? Younger?) to lie about their age so they could join early?

Modern numbers suggest 250 000, though I've seen no source for it; it's not too hard to imagine, many of the 15-17 year olds in Britain in 1914 would have come of age by 1915-18 and would be eligible for enlistment/conscription. Considering differences in height etc, it might seem appalling to us today, but at the time mistakes and 'oversights' could be made. In fact, the youngest soldier in WWI was an 8 year old who served in the Serbian Army, Momcilo Gavric, who achieved the rank of sergeant, was wounded in battle, and was decorated for bravery; he died at age 86.

As Catriona Pennell mentions in this lecture [here] (http://podcasts.ox.ac.uk/rethinking-british-volunteerism-1914-rush-colours), the greatest rush of enlistment in 1914 did not take place until the first week of September, and large numbers of men were turned back, either for lack of doctors to examine them, or because they failed to pass inspection. As I've noted in answers such as [this one] (https://www.reddit.com/r/AskHistorians/comments/3dudse/were_citizens_aware_of_the_military/), the idea of 'war enthusiasm' is a myth, though large numbers of men did enlist.

That said, from what I've read of underage recruits, they were sent home in large numbers, and I've only seen a few like 13 year old Sidney Lewis who served through the whole war. It ought to be noted here that the BEF also had to send 500 000 soldiers, who were not under aged, back to Britain in 1915 to work in the war industry.