## Some important l.c.m. and h.c.f. tricks

1) Product of two numbers = Their h.c.f. * Their l.c.m.

2) h.c.f. of given numbers always divides their l.c.m.

3) h.c.f. of given fractions = h.c.f. of numerator / l.c.m. of denominator

4) l.c.m. of given fractions = l.c.m. of numerator / h.c.f. of denominator

5) If d is the h.c.f. of two positive integer a and b, then there exist unique integer m and n, such that

d = am + bn

6) If p is prime and a,b are any integer then P / ab ,This implies P / a or P / b

7) h.c.f. of a given number always divides its l.c.m.