What is the Least Common Multiple of 13972 and 13984?

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 13972 and 13984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13972 and 13984, than apply into the LCM equation.

GCF(13972,13984) = 4
LCM(13972,13984) = ( 13972 × 13984) / 4
LCM(13972,13984) = 195384448 / 4
LCM(13972,13984) = 48846112

Least Common Multiple (LCM) of 13972 and 13984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13972 and 13984. First we will calculate the prime factors of 13972 and 13984.

Prime Factorization of 13972

Prime Factorization of 13984

Now multiplying the highest exponent prime factors to calculate the LCM of 13972 and 13984.

LCM(13972,13984) = 2⁵ × 7¹ × 499¹ × 19¹ × 23¹
LCM(13972,13984) = 48846112