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What is the Least Common Multiple of 3201 and 3210?

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 (LCM) of 3201 and 3210 is 3425070.

LCM(3201,3210) = 3425070

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Least Common Multiple of 3201 and 3210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3201 and 3210, than apply into the LCM equation.

GCF(3201,3210) = 3
LCM(3201,3210) = ( 3201 × 3210) / 3
LCM(3201,3210) = 10275210 / 3
LCM(3201,3210) = 3425070

Least Common Multiple (LCM) of 3201 and 3210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3201 and 3210. First we will calculate the prime factors of 3201 and 3210.

Prime Factorization of 3201

Prime factors of 3201 are 3, 11, 97. Prime factorization of 3201 in exponential form is:

3201 = 31 × 111 × 971

Prime Factorization of 3210

Prime factors of 3210 are 2, 3, 5, 107. Prime factorization of 3210 in exponential form is:

3210 = 21 × 31 × 51 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 3201 and 3210.

LCM(3201,3210) = 31 × 111 × 971 × 21 × 51 × 1071
LCM(3201,3210) = 3425070