What is the Least Common Multiple of 1535 and 1540?

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 1535 and 1540 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1535 and 1540, than apply into the LCM equation.

GCF(1535,1540) = 5
LCM(1535,1540) = ( 1535 × 1540) / 5
LCM(1535,1540) = 2363900 / 5
LCM(1535,1540) = 472780

Least Common Multiple (LCM) of 1535 and 1540 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1535 and 1540. First we will calculate the prime factors of 1535 and 1540.

Prime Factorization of 1535

Prime Factorization of 1540

Now multiplying the highest exponent prime factors to calculate the LCM of 1535 and 1540.

LCM(1535,1540) = 5¹ × 307¹ × 2² × 7¹ × 11¹
LCM(1535,1540) = 472780