Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 916 and 920 the smallest integer that is 210680 that is divisible by both numbers.
Least Common Multiple (LCM) of 916 and 920 is 210680.
LCM(916,920) = 210680
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 916 and 920. First we will calculate the prime factors of 916 and 920.
Prime Factorization of 916
2 | 916 |
2 | 458 |
229 | 229 |
1 |
Prime factors of 916 are 2,229. Prime factorization of 916 in exponential form is:
916 = 22×2291
Prime Factorization of 920
2 | 920 |
2 | 460 |
2 | 230 |
5 | 115 |
23 | 23 |
1 |
Prime factors of 920 are 2, 5,23. Prime factorization of 920 in exponential form is:
920 = 23×51×231
Now multiplying the highest exponent prime factors to calculate the LCM of 916 and 920.
LCM(916,920) = 23×51×231×2291
LCM(916,920) = 210680
Factors of 916
List of positive integer factors of 916 that divides 916 without a remainder.
1, 2, 4, 229, 458, 916
Factors of 920
List of positive integer factors of 920 that divides 920 without a remainder.
1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 916 and 920, than apply into the LCM equation.
GCF(916,920) = 4
LCM(916,920) = ( 916 × 920) / 4
LCM(916,920) = 842720 / 4
LCM(916,920) = 210680
(i) The LCM of 920 and 916 is associative
LCM of 916 and 920 = LCM of 920 and 916
1. What is the LCM of 916 and 920?
Answer: LCM of 916 and 920 is 210680.
2. What are the Factors of 916?
Answer: Factors of 916 are 1, 2, 4, 229, 458, 916. There are 6 integers that are factors of 916. The greatest factor of 916 is 916.
3. What are the Factors of 920?
Answer: Factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920. There are 16 integers that are factors of 920. The greatest factor of 920 is 920.
4. How to Find the LCM of 916 and 920?
Answer:
Least Common Multiple of 916 and 920 = 210680
Step 1: Find the prime factorization of 916
916 = 2 x 2 x 229
Step 2: Find the prime factorization of 920
920 = 2 x 2 x 2 x 5 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 210680 = 2 x 2 x 2 x 5 x 23 x 229
Step 4: Therefore, the least common multiple of 916 and 920 is 210680.