Least Common Multiple of 110 and 111
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 111 the smallest integer that is 12210 that is divisible by both numbers.
Least Common Multiple (LCM) of 110 and 111 is 12210.
LCM(110,111) = 12210
LCM of 110 and 111
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 110 and 111 by Prime method
- Least Common Multiple of 110 and 111 with GCF Formula
LCM of 110 and 111 is 12210
Least common multiple can be found by multiplying the highest exponent prime factors of 110 and 111. First we will calculate the prime factors of 110 and 111.
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 111
| 3 | 111 |
| 37 | 37 |
| 1 |
Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:
111 = 31×371
Now multiplying the highest exponent prime factors to calculate the LCM of 110 and 111.
LCM(110,111) = 21×31×51×111×371
LCM(110,111) = 12210
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 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Least Common Multiple of 110 and 111 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 110 and 111, than apply into the LCM equation.
GCF(110,111) = 1
LCM(110,111) = ( 110 × 111) / 1
LCM(110,111) = 12210 / 1
LCM(110,111) = 12210
Properties of LCM 110 and 111
(i) The LCM of 111 and 110 is associative
LCM of 110 and 111 = LCM of 111 and 110
Related Least Common Multiples of 110
Related Least Common Multiples of 111
Frequently Asked Questions on LCM of 110 and 111
1. What is the LCM of 110 and 111?
Answer: LCM of 110 and 111 is 12210.
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 111?
Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.
4. How to Find the LCM of 110 and 111?
Answer:
Least Common Multiple of 110 and 111 = 12210
Step 1: Find the prime factorization of 110
110 = 2 x 5 x 11
Step 2: Find the prime factorization of 111
111 = 3 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12210 = 2 x 3 x 5 x 11 x 37
Step 4: Therefore, the least common multiple of 110 and 111 is 12210.
