Least Common Multiple of 105 and 106
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 106 the smallest integer that is 11130 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 106 is 11130.
LCM(105,106) = 11130
LCM of 105 and 106
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 106 by Prime method
- Least Common Multiple of 105 and 106 with GCF Formula
LCM of 105 and 106 is 11130
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 106. First we will calculate the prime factors of 105 and 106.
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 106
| 2 | 106 |
| 53 | 53 |
| 1 |
Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:
106 = 21×531
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 106.
LCM(105,106) = 21×31×51×71×531
LCM(105,106) = 11130
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 106
List of positive integer factors of 106 that divides 106 without a remainder.
1, 2, 53, 106
Least Common Multiple of 105 and 106 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 106, than apply into the LCM equation.
GCF(105,106) = 1
LCM(105,106) = ( 105 × 106) / 1
LCM(105,106) = 11130 / 1
LCM(105,106) = 11130
Properties of LCM 105 and 106
(i) The LCM of 106 and 105 is associative
LCM of 105 and 106 = LCM of 106 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 106
Frequently Asked Questions on LCM of 105 and 106
1. What is the LCM of 105 and 106?
Answer: LCM of 105 and 106 is 11130.
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 106?
Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.
4. How to Find the LCM of 105 and 106?
Answer:
Least Common Multiple of 105 and 106 = 11130
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 106
106 = 2 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11130 = 2 x 3 x 5 x 7 x 53
Step 4: Therefore, the least common multiple of 105 and 106 is 11130.
