Least Common Multiple of 101 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 101 and 106 the smallest integer that is 10706 that is divisible by both numbers.
Least Common Multiple (LCM) of 101 and 106 is 10706.
LCM(101,106) = 10706
LCM of 101 and 106
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 101 and 106 by Prime method
- Least Common Multiple of 101 and 106 with GCF Formula
LCM of 101 and 106 is 10706
Least common multiple can be found by multiplying the highest exponent prime factors of 101 and 106. First we will calculate the prime factors of 101 and 106.
Prime Factorization of 101
| 101 | 101 |
| 1 |
Prime factors of 101 are 101. Prime factorization of 101 in exponential form is:
101 = 1011
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 101 and 106.
LCM(101,106) = 21×531×1011
LCM(101,106) = 10706
Factors of 101
List of positive integer factors of 101 that divides 101 without a remainder.
1, 101
Factors of 106
List of positive integer factors of 106 that divides 106 without a remainder.
1, 2, 53, 106
Least Common Multiple of 101 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 101 and 106, than apply into the LCM equation.
GCF(101,106) = 1
LCM(101,106) = ( 101 × 106) / 1
LCM(101,106) = 10706 / 1
LCM(101,106) = 10706
Properties of LCM 101 and 106
(i) The LCM of 106 and 101 is associative
LCM of 101 and 106 = LCM of 106 and 101
Related Least Common Multiples of 101
Related Least Common Multiples of 106
Frequently Asked Questions on LCM of 101 and 106
1. What is the LCM of 101 and 106?
Answer: LCM of 101 and 106 is 10706.
2. What are the Factors of 101?
Answer: Factors of 101 are 1, 101. There are 2 integers that are factors of 101. The greatest factor of 101 is 101.
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 101 and 106?
Answer:
Least Common Multiple of 101 and 106 = 10706
Step 1: Find the prime factorization of 101
101 = 101
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 = 10706 = 2 x 53 x 101
Step 4: Therefore, the least common multiple of 101 and 106 is 10706.
