Least Common Multiple of 105 and 108
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 108 the smallest integer that is 3780 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 108 is 3780.
LCM(105,108) = 3780
LCM of 105 and 108
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 108 by Prime method
- Least Common Multiple of 105 and 108 with GCF Formula
LCM of 105 and 108 is 3780
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 108. First we will calculate the prime factors of 105 and 108.
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 108
| 2 | 108 |
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:
108 = 22×33
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 108.
LCM(105,108) = 22×33×51×71
LCM(105,108) = 3780
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 108
List of positive integer factors of 108 that divides 108 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Least Common Multiple of 105 and 108 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 108, than apply into the LCM equation.
GCF(105,108) = 3
LCM(105,108) = ( 105 × 108) / 3
LCM(105,108) = 11340 / 3
LCM(105,108) = 3780
Properties of LCM 105 and 108
(i) The LCM of 108 and 105 is associative
LCM of 105 and 108 = LCM of 108 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 108
Frequently Asked Questions on LCM of 105 and 108
1. What is the LCM of 105 and 108?
Answer: LCM of 105 and 108 is 3780.
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 108?
Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.
4. How to Find the LCM of 105 and 108?
Answer:
Least Common Multiple of 105 and 108 = 3780
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 108
108 = 2 x 2 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3780 = 2 x 2 x 3 x 3 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 105 and 108 is 3780.
