Least Common Multiple of 105 and 107
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 107 the smallest integer that is 11235 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 107 is 11235.
LCM(105,107) = 11235
LCM of 105 and 107
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 107 by Prime method
- Least Common Multiple of 105 and 107 with GCF Formula
LCM of 105 and 107 is 11235
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 107. First we will calculate the prime factors of 105 and 107.
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 107
| 107 | 107 |
| 1 |
Prime factors of 107 are 107. Prime factorization of 107 in exponential form is:
107 = 1071
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 107.
LCM(105,107) = 31×51×71×1071
LCM(105,107) = 11235
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 107
List of positive integer factors of 107 that divides 107 without a remainder.
1, 107
Least Common Multiple of 105 and 107 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 107, than apply into the LCM equation.
GCF(105,107) = 1
LCM(105,107) = ( 105 × 107) / 1
LCM(105,107) = 11235 / 1
LCM(105,107) = 11235
Properties of LCM 105 and 107
(i) The LCM of 107 and 105 is associative
LCM of 105 and 107 = LCM of 107 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 107
Frequently Asked Questions on LCM of 105 and 107
1. What is the LCM of 105 and 107?
Answer: LCM of 105 and 107 is 11235.
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 107?
Answer: Factors of 107 are 1, 107. There are 2 integers that are factors of 107. The greatest factor of 107 is 107.
4. How to Find the LCM of 105 and 107?
Answer:
Least Common Multiple of 105 and 107 = 11235
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 107
107 = 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11235 = 3 x 5 x 7 x 107
Step 4: Therefore, the least common multiple of 105 and 107 is 11235.
