What is the Least Common Multiple of 742 and 752?

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 742 and 752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 742 and 752, than apply into the LCM equation.

GCF(742,752) = 2
LCM(742,752) = ( 742 × 752) / 2
LCM(742,752) = 557984 / 2
LCM(742,752) = 278992

Least Common Multiple (LCM) of 742 and 752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 742 and 752. First we will calculate the prime factors of 742 and 752.

Prime Factorization of 742

Prime Factorization of 752

Now multiplying the highest exponent prime factors to calculate the LCM of 742 and 752.

LCM(742,752) = 2⁴ × 7¹ × 53¹ × 47¹
LCM(742,752) = 278992