What is the Least Common Multiple of 600 and 610?
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 600 and 610 is 36600.
LCM(600,610) = 36600
Least Common Multiple of 600 and 610 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 600 and 610, than apply into the LCM equation.
GCF(600,610) = 10
LCM(600,610) = ( 600 × 610) / 10
LCM(600,610) = 366000 / 10
LCM(600,610) = 36600
Least Common Multiple (LCM) of 600 and 610 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 600 and 610. First we will calculate the prime factors of 600 and 610.
Prime Factorization of 600
Prime factors of 600 are 2, 3, 5. Prime factorization of 600 in exponential form is:
600 = 23 × 31 × 52
Prime Factorization of 610
Prime factors of 610 are 2, 5, 61. Prime factorization of 610 in exponential form is:
610 = 21 × 51 × 611
Now multiplying the highest exponent prime factors to calculate the LCM of 600 and 610.
LCM(600,610) = 23 × 31 × 52 × 611
LCM(600,610) = 36600
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