What is the Least Common Multiple of 1460 and 1474?

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 1460 and 1474 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1460 and 1474, than apply into the LCM equation.

GCF(1460,1474) = 2
LCM(1460,1474) = ( 1460 × 1474) / 2
LCM(1460,1474) = 2152040 / 2
LCM(1460,1474) = 1076020

Least Common Multiple (LCM) of 1460 and 1474 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1460 and 1474. First we will calculate the prime factors of 1460 and 1474.

Prime Factorization of 1460

Prime Factorization of 1474

Now multiplying the highest exponent prime factors to calculate the LCM of 1460 and 1474.

LCM(1460,1474) = 2² × 5¹ × 73¹ × 11¹ × 67¹
LCM(1460,1474) = 1076020