What is the Least Common Multiple of 17205 and 17210?
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 17205 and 17210 is 59219610.
LCM(17205,17210) = 59219610
Least Common Multiple of 17205 and 17210 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17205 and 17210, than apply into the LCM equation.
GCF(17205,17210) = 5
LCM(17205,17210) = ( 17205 × 17210) / 5
LCM(17205,17210) = 296098050 / 5
LCM(17205,17210) = 59219610
Least Common Multiple (LCM) of 17205 and 17210 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 17205 and 17210. First we will calculate the prime factors of 17205 and 17210.
Prime Factorization of 17205
Prime factors of 17205 are 3, 5, 31, 37. Prime factorization of 17205 in exponential form is:
17205 = 31 × 51 × 311 × 371
Prime Factorization of 17210
Prime factors of 17210 are 2, 5, 1721. Prime factorization of 17210 in exponential form is:
17210 = 21 × 51 × 17211
Now multiplying the highest exponent prime factors to calculate the LCM of 17205 and 17210.
LCM(17205,17210) = 31 × 51 × 311 × 371 × 21 × 17211
LCM(17205,17210) = 59219610
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