What is the Least Common Multiple of 51972 and 51984?

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 51972 and 51984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51972 and 51984, than apply into the LCM equation.

GCF(51972,51984) = 12
LCM(51972,51984) = ( 51972 × 51984) / 12
LCM(51972,51984) = 2701712448 / 12
LCM(51972,51984) = 225142704

Least Common Multiple (LCM) of 51972 and 51984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51972 and 51984. First we will calculate the prime factors of 51972 and 51984.

Prime Factorization of 51972

Prime Factorization of 51984

Now multiplying the highest exponent prime factors to calculate the LCM of 51972 and 51984.

LCM(51972,51984) = 2⁴ × 3² × 61¹ × 71¹ × 19²
LCM(51972,51984) = 225142704