What is the LCM of 1100 and 2017
Answers
Least Common Multiple (LCM) of 1100 and 2017 is 2218700.
LCM(1100,2017) = 2218700
Least common multiple can be found by multiplying the highest exponent prime factors of 1100 and 2017. First we will calculate the prime factors of 1100 and 2017.
Prime Factorization of 1100
2 1100
2 550
5 275
5 55
11 11
1
Prime factors of 1100 are 2, 5,11. Prime factorization of 1100 in exponential form is:
1100 = 22×52×111
Prime Factorization of 2017
2017 2017
1
Prime factors of 2017 are 2017. Prime factorization of 2017 in exponential form is:
2017 = 20171
Now multiplying the highest exponent prime factors to calculate the LCM of 1100 and 2017.
LCM(1100,2017) = 22×52×111×20171
LCM(1100,2017) = 2218700
Factors of 1100
List of positive integer factors of 1100 that divides 1100 without a remainder.
1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100
Factors of 2017
List of positive integer factors of 2017 that divides 2017 without a remainder.
1, 2017
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1100 and 2017, than apply into the LCM equation.
GCF(1100,2017) = 1
LCM(1100,2017) = ( 1100 × 2017) / 1
LCM(1100,2017) = 2218700 / 1
LCM(1100,2017) = 2218700
Answer: 2, 218, 700
Step-by-step explanation:
Solved with Cake Method.
You are to divide your numbers by prime numbers as long as both numbers are evenly divisible by that prime number.
Cake: 1100 Ladder: 2017
The LCM is the product of your numbers because there are no primes that divide evenly into both of them.
LCM: 1100 x 2017
LCM: 2,218,700
So, LCM(1100, 2017) = 2,228,700