What is the Least Common Multiple of 27968 and 27974?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 27968 and 27974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27968 and 27974, than apply into the LCM equation.

GCF(27968,27974) = 2
LCM(27968,27974) = ( 27968 × 27974) / 2
LCM(27968,27974) = 782376832 / 2
LCM(27968,27974) = 391188416

Least Common Multiple (LCM) of 27968 and 27974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27968 and 27974. First we will calculate the prime factors of 27968 and 27974.

Prime Factorization of 27968

Prime Factorization of 27974

Now multiplying the highest exponent prime factors to calculate the LCM of 27968 and 27974.

LCM(27968,27974) = 2⁶ × 19¹ × 23¹ × 71¹ × 197¹
LCM(27968,27974) = 391188416