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Anne and Jane started a new job on the same day. The job requires field work but they need to work at the home office
on a specified day. Ann is to work at the home office every 10-th days and Jane is to work at the office every 12-th days.
On what day will they meet at the office?
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To answer the question, you should find the day (the number) which is multiple of 10 and 12.
More precisely, you need to find least such a number.
Such number is called Least Common Multiple (abbreviation is LCM).
LCM of the numbers 10 and 12 is 60.
To find it, you consider decomposition of the numbers 10 and 12 into the product of prime divisors
10 = 2*5, 12 = 2^2*3,
and take then the product of these prime divisors 2, 3 and 5 in maximum degrees
which you see in their decompositions LCM = 2^2^3*5 = 4*3*5 = 12*5 = 60. ANSWER
Solved, answered and explained.