What is the Least Common Multiple of 23744 and 23754?

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 23744 and 23754 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23744 and 23754, than apply into the LCM equation.

GCF(23744,23754) = 2
LCM(23744,23754) = ( 23744 × 23754) / 2
LCM(23744,23754) = 564014976 / 2
LCM(23744,23754) = 282007488

Least Common Multiple (LCM) of 23744 and 23754 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23744 and 23754. First we will calculate the prime factors of 23744 and 23754.

Prime Factorization of 23744

Prime Factorization of 23754

Now multiplying the highest exponent prime factors to calculate the LCM of 23744 and 23754.

LCM(23744,23754) = 2⁶ × 7¹ × 53¹ × 3¹ × 37¹ × 107¹
LCM(23744,23754) = 282007488