Least Common Multiple of 105 and 110
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 105 and 110 the smallest integer that is 2310 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 110 is 2310.
LCM(105,110) = 2310
LCM of 105 and 110
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 110 by Prime method
- Least Common Multiple of 105 and 110 with GCF Formula
LCM of 105 and 110 is 2310
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 110. First we will calculate the prime factors of 105 and 110.
Prime Factorization of 105
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 105 are 3, 5,7. Prime factorization of 105 in exponential form is:
105 = 31×51×71
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
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 110.
LCM(105,110) = 21×31×51×71×111
LCM(105,110) = 2310
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1, 3, 5, 7, 15, 21, 35, 105
Factors of 110
List of positive integer factors of 110 that divides 110 without a remainder.
1, 2, 5, 10, 11, 22, 55, 110
Least Common Multiple of 105 and 110 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 110, than apply into the LCM equation.
GCF(105,110) = 5
LCM(105,110) = ( 105 × 110) / 5
LCM(105,110) = 11550 / 5
LCM(105,110) = 2310
Properties of LCM 105 and 110
(i) The LCM of 110 and 105 is associative
LCM of 105 and 110 = LCM of 110 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 110
Frequently Asked Questions on LCM of 105 and 110
1. What is the LCM of 105 and 110?
Answer: LCM of 105 and 110 is 2310.
2. What are the Factors of 105?
Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.
3. 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.
4. How to Find the LCM of 105 and 110?
Answer:
Least Common Multiple of 105 and 110 = 2310
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 110
110 = 2 x 5 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2310 = 2 x 3 x 5 x 7 x 11
Step 4: Therefore, the least common multiple of 105 and 110 is 2310.