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What is the Least Common Multiple of 7201 and 7214?

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 7201 and 7214 is 51948014.

LCM(7201,7214) = 51948014

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Least Common Multiple of 7201 and 7214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7201 and 7214, than apply into the LCM equation.

GCF(7201,7214) = 1
LCM(7201,7214) = ( 7201 × 7214) / 1
LCM(7201,7214) = 51948014 / 1
LCM(7201,7214) = 51948014

Least Common Multiple (LCM) of 7201 and 7214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7201 and 7214. First we will calculate the prime factors of 7201 and 7214.

Prime Factorization of 7201

Prime factors of 7201 are 19, 379. Prime factorization of 7201 in exponential form is:

7201 = 191 × 3791

Prime Factorization of 7214

Prime factors of 7214 are 2, 3607. Prime factorization of 7214 in exponential form is:

7214 = 21 × 36071

Now multiplying the highest exponent prime factors to calculate the LCM of 7201 and 7214.

LCM(7201,7214) = 191 × 3791 × 21 × 36071
LCM(7201,7214) = 51948014