What is the Least Common Multiple of 1490 and 1509?

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 1490 and 1509 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1490 and 1509, than apply into the LCM equation.

GCF(1490,1509) = 1
LCM(1490,1509) = ( 1490 × 1509) / 1
LCM(1490,1509) = 2248410 / 1
LCM(1490,1509) = 2248410

Least Common Multiple (LCM) of 1490 and 1509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1490 and 1509. First we will calculate the prime factors of 1490 and 1509.

Prime Factorization of 1490

Prime Factorization of 1509

Now multiplying the highest exponent prime factors to calculate the LCM of 1490 and 1509.

LCM(1490,1509) = 2¹ × 5¹ × 149¹ × 3¹ × 503¹
LCM(1490,1509) = 2248410