maths....(mathematics..)
posted by .... .
by prime factorisation method find the least positive number divisible by 700 and 364

First you have to prime factorize both numbers. The greatest common divisor(GCD) has the
lower number of prime factors that appear in both lists.
2 appears twice and 7 appears once on both lists 5,7 and 13 appear on one list only, so they and not "common" factors and do not appear in the GCD
364 = 91*4 = 2^2 * 7 * 13
700 = 2^2 * 5^2 * 7
GCD = 2^2 * 7 = 28 
700 = 7x2x2x5x5
364 = 2x2x91
HCM = 7x2x2x5x5x91 = 63700 
I assumed 91 was prime, ...
700 = 7x2x2x5x5
364 = 2x2x7x13
LCM = 7x2x2x2x2x13 = 9100 
I read the problem incorrectly