What is the Least Common Multiple of 360 and 366?
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 360 and 366 is 21960.
LCM(360,366) = 21960
Least Common Multiple of 360 and 366 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 360 and 366, than apply into the LCM equation.
GCF(360,366) = 6
LCM(360,366) = ( 360 × 366) / 6
LCM(360,366) = 131760 / 6
LCM(360,366) = 21960
Least Common Multiple (LCM) of 360 and 366 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 360 and 366. First we will calculate the prime factors of 360 and 366.
Prime Factorization of 360
Prime factors of 360 are 2, 3, 5. Prime factorization of 360 in exponential form is:
360 = 23 × 32 × 51
Prime Factorization of 366
Prime factors of 366 are 2, 3, 61. Prime factorization of 366 in exponential form is:
366 = 21 × 31 × 611
Now multiplying the highest exponent prime factors to calculate the LCM of 360 and 366.
LCM(360,366) = 23 × 32 × 51 × 611
LCM(360,366) = 21960
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