GCF and LCM Calculator Logo

What is the Least Common Multiple of 705 and 715?

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 705 and 715 is 100815.

LCM(705,715) = 100815

LCM Calculator and
and

Least Common Multiple of 705 and 715 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 705 and 715, than apply into the LCM equation.

GCF(705,715) = 5
LCM(705,715) = ( 705 × 715) / 5
LCM(705,715) = 504075 / 5
LCM(705,715) = 100815

Least Common Multiple (LCM) of 705 and 715 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 705 and 715. First we will calculate the prime factors of 705 and 715.

Prime Factorization of 705

Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:

705 = 31 × 51 × 471

Prime Factorization of 715

Prime factors of 715 are 5, 11, 13. Prime factorization of 715 in exponential form is:

715 = 51 × 111 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 705 and 715.

LCM(705,715) = 31 × 51 × 471 × 111 × 131
LCM(705,715) = 100815