What is the Least Common Multiple of 33972 and 33984?

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 33972 and 33984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33972 and 33984, than apply into the LCM equation.

GCF(33972,33984) = 12
LCM(33972,33984) = ( 33972 × 33984) / 12
LCM(33972,33984) = 1154504448 / 12
LCM(33972,33984) = 96208704

Least Common Multiple (LCM) of 33972 and 33984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33972 and 33984. First we will calculate the prime factors of 33972 and 33984.

Prime Factorization of 33972

Prime Factorization of 33984

Now multiplying the highest exponent prime factors to calculate the LCM of 33972 and 33984.

LCM(33972,33984) = 2⁶ × 3² × 19¹ × 149¹ × 59¹
LCM(33972,33984) = 96208704