Least Common Multiple of 86 and 105
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 86 and 105 the smallest integer that is 9030 that is divisible by both numbers.
Least Common Multiple (LCM) of 86 and 105 is 9030.
LCM(86,105) = 9030
LCM of 86 and 105
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 86 and 105 by Prime method
- Least Common Multiple of 86 and 105 with GCF Formula
LCM of 86 and 105 is 9030
Least common multiple can be found by multiplying the highest exponent prime factors of 86 and 105. First we will calculate the prime factors of 86 and 105.
Prime Factorization of 86
| 2 | 86 |
| 43 | 43 |
| 1 |
Prime factors of 86 are 2,43. Prime factorization of 86 in exponential form is:
86 = 21×431
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
Now multiplying the highest exponent prime factors to calculate the LCM of 86 and 105.
LCM(86,105) = 21×31×51×71×431
LCM(86,105) = 9030
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1, 2, 43, 86
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1, 3, 5, 7, 15, 21, 35, 105
Least Common Multiple of 86 and 105 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 86 and 105, than apply into the LCM equation.
GCF(86,105) = 1
LCM(86,105) = ( 86 × 105) / 1
LCM(86,105) = 9030 / 1
LCM(86,105) = 9030
Properties of LCM 86 and 105
(i) The LCM of 105 and 86 is associative
LCM of 86 and 105 = LCM of 105 and 86
Related Least Common Multiples of 86
Related Least Common Multiples of 105
Frequently Asked Questions on LCM of 86 and 105
1. What is the LCM of 86 and 105?
Answer: LCM of 86 and 105 is 9030.
2. What are the Factors of 86?
Answer: Factors of 86 are 1, 2, 43, 86. There are 4 integers that are factors of 86. The greatest factor of 86 is 86.
3. 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.
4. How to Find the LCM of 86 and 105?
Answer:
Least Common Multiple of 86 and 105 = 9030
Step 1: Find the prime factorization of 86
86 = 2 x 43
Step 2: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9030 = 2 x 3 x 5 x 7 x 43
Step 4: Therefore, the least common multiple of 86 and 105 is 9030.