What is the Least Common Multiple of 5460 and 5470?

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 5460 and 5470 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5460 and 5470, than apply into the LCM equation.

GCF(5460,5470) = 10
LCM(5460,5470) = ( 5460 × 5470) / 10
LCM(5460,5470) = 29866200 / 10
LCM(5460,5470) = 2986620

Least Common Multiple (LCM) of 5460 and 5470 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5460 and 5470. First we will calculate the prime factors of 5460 and 5470.

Prime Factorization of 5460

Prime Factorization of 5470

Now multiplying the highest exponent prime factors to calculate the LCM of 5460 and 5470.

LCM(5460,5470) = 2² × 3¹ × 5¹ × 7¹ × 13¹ × 547¹
LCM(5460,5470) = 2986620