What is the Least Common Multiple of 1461 and 1470?

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 1461 and 1470 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1461 and 1470, than apply into the LCM equation.

GCF(1461,1470) = 3
LCM(1461,1470) = ( 1461 × 1470) / 3
LCM(1461,1470) = 2147670 / 3
LCM(1461,1470) = 715890

Least Common Multiple (LCM) of 1461 and 1470 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1461 and 1470. First we will calculate the prime factors of 1461 and 1470.

Prime Factorization of 1461

Prime Factorization of 1470

Now multiplying the highest exponent prime factors to calculate the LCM of 1461 and 1470.

LCM(1461,1470) = 3¹ × 487¹ × 2¹ × 5¹ × 7²
LCM(1461,1470) = 715890