What is the Least Common Multiple of 53400 and 53408?

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 53400 and 53408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 53400 and 53408, than apply into the LCM equation.

GCF(53400,53408) = 8
LCM(53400,53408) = ( 53400 × 53408) / 8
LCM(53400,53408) = 2851987200 / 8
LCM(53400,53408) = 356498400

Least Common Multiple (LCM) of 53400 and 53408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 53400 and 53408. First we will calculate the prime factors of 53400 and 53408.

Prime Factorization of 53400

Prime Factorization of 53408

Now multiplying the highest exponent prime factors to calculate the LCM of 53400 and 53408.

LCM(53400,53408) = 2⁵ × 3¹ × 5² × 89¹ × 1669¹
LCM(53400,53408) = 356498400