What is the Least Common Multiple of 13968 and 13974?

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 13968 and 13974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13968 and 13974, than apply into the LCM equation.

GCF(13968,13974) = 6
LCM(13968,13974) = ( 13968 × 13974) / 6
LCM(13968,13974) = 195188832 / 6
LCM(13968,13974) = 32531472

Least Common Multiple (LCM) of 13968 and 13974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13968 and 13974. First we will calculate the prime factors of 13968 and 13974.

Prime Factorization of 13968

Prime Factorization of 13974

Now multiplying the highest exponent prime factors to calculate the LCM of 13968 and 13974.

LCM(13968,13974) = 2⁴ × 3² × 97¹ × 17¹ × 137¹
LCM(13968,13974) = 32531472