Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 110 and 115 the smallest integer that is 2530 that is divisible by both numbers.
Least Common Multiple (LCM) of 110 and 115 is 2530.
LCM(110,115) = 2530
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 110 and 115. First we will calculate the prime factors of 110 and 115.
Prime Factorization of 110
2 | 110 |
5 | 55 |
11 | 11 |
1 |
Prime factors of 110 are 2, 5,11. Prime factorization of 110 in exponential form is:
110 = 21×51×111
Prime Factorization of 115
5 | 115 |
23 | 23 |
1 |
Prime factors of 115 are 5,23. Prime factorization of 115 in exponential form is:
115 = 51×231
Now multiplying the highest exponent prime factors to calculate the LCM of 110 and 115.
LCM(110,115) = 21×51×111×231
LCM(110,115) = 2530
Factors of 110
List of positive integer factors of 110 that divides 110 without a remainder.
1, 2, 5, 10, 11, 22, 55, 110
Factors of 115
List of positive integer factors of 115 that divides 115 without a remainder.
1, 5, 23, 115
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 110 and 115, than apply into the LCM equation.
GCF(110,115) = 5
LCM(110,115) = ( 110 × 115) / 5
LCM(110,115) = 12650 / 5
LCM(110,115) = 2530
(i) The LCM of 115 and 110 is associative
LCM of 110 and 115 = LCM of 115 and 110
1. What is the LCM of 110 and 115?
Answer: LCM of 110 and 115 is 2530.
2. What are the Factors of 110?
Answer: Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. There are 8 integers that are factors of 110. The greatest factor of 110 is 110.
3. What are the Factors of 115?
Answer: Factors of 115 are 1, 5, 23, 115. There are 4 integers that are factors of 115. The greatest factor of 115 is 115.
4. How to Find the LCM of 110 and 115?
Answer:
Least Common Multiple of 110 and 115 = 2530
Step 1: Find the prime factorization of 110
110 = 2 x 5 x 11
Step 2: Find the prime factorization of 115
115 = 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 = 2530 = 2 x 5 x 11 x 23
Step 4: Therefore, the least common multiple of 110 and 115 is 2530.