What is the Least Common Multiple of 1540 and 1549?

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 1540 and 1549 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1540 and 1549, than apply into the LCM equation.

GCF(1540,1549) = 1
LCM(1540,1549) = ( 1540 × 1549) / 1
LCM(1540,1549) = 2385460 / 1
LCM(1540,1549) = 2385460

Least Common Multiple (LCM) of 1540 and 1549 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1540 and 1549. First we will calculate the prime factors of 1540 and 1549.

Prime Factorization of 1540

Prime Factorization of 1549

Now multiplying the highest exponent prime factors to calculate the LCM of 1540 and 1549.

LCM(1540,1549) = 2² × 5¹ × 7¹ × 11¹ × 1549¹
LCM(1540,1549) = 2385460