Factors and Multiples: If a number
a divides another number
b exactly, we say that
a is a factor of
b. In this case,
b is called a multiple of
a.
Highest Common Factor (H.C.F) or Greatest Common Measure (G.C.M) or Greatest Common Divisor (G.C.D):

Factorization Method: Express each of the given numbers as the product of prime factors. The product of least powers of common prime factors is H.C.F.

Division Method: Divide larger number by smaller one. Now, divide the divisor by the remainder. And repeat it until the remainder is till zero. The last divisor is H.C.F.
Least Common Multiple (L.C.M):

Factorization Method: Each one of the given numbers into a product of prime factors. L.C.M. is the product of highest powers of all the factors.

Common division Method: Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat it till no two of the numbers are divisible by the same number except 1. The L.C.M is product of divisors and undivided numbers.
Product of two numbers = Product of their H.C.F and L.C.M.
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