What is the Least Common Multiple of 1456 and 1460?

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 1456 and 1460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1456 and 1460, than apply into the LCM equation.

GCF(1456,1460) = 4
LCM(1456,1460) = ( 1456 × 1460) / 4
LCM(1456,1460) = 2125760 / 4
LCM(1456,1460) = 531440

Least Common Multiple (LCM) of 1456 and 1460 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1456 and 1460. First we will calculate the prime factors of 1456 and 1460.

Prime Factorization of 1456

Prime Factorization of 1460

Now multiplying the highest exponent prime factors to calculate the LCM of 1456 and 1460.

LCM(1456,1460) = 2⁴ × 7¹ × 13¹ × 5¹ × 73¹
LCM(1456,1460) = 531440