Least Common Multiple of 101 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 101 and 105 the smallest integer that is 10605 that is divisible by both numbers.
Least Common Multiple (LCM) of 101 and 105 is 10605.
LCM(101,105) = 10605
LCM of 101 and 105
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 101 and 105 by Prime method
- Least Common Multiple of 101 and 105 with GCF Formula
LCM of 101 and 105 is 10605
Least common multiple can be found by multiplying the highest exponent prime factors of 101 and 105. First we will calculate the prime factors of 101 and 105.
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 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 101 and 105.
LCM(101,105) = 31×51×71×1011
LCM(101,105) = 10605
Factors of 101
List of positive integer factors of 101 that divides 101 without a remainder.
1, 101
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 101 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 101 and 105, than apply into the LCM equation.
GCF(101,105) = 1
LCM(101,105) = ( 101 × 105) / 1
LCM(101,105) = 10605 / 1
LCM(101,105) = 10605
Properties of LCM 101 and 105
(i) The LCM of 105 and 101 is associative
LCM of 101 and 105 = LCM of 105 and 101
Related Least Common Multiples of 101
Related Least Common Multiples of 105
Frequently Asked Questions on LCM of 101 and 105
1. What is the LCM of 101 and 105?
Answer: LCM of 101 and 105 is 10605.
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 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 101 and 105?
Answer:
Least Common Multiple of 101 and 105 = 10605
Step 1: Find the prime factorization of 101
101 = 101
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 = 10605 = 3 x 5 x 7 x 101
Step 4: Therefore, the least common multiple of 101 and 105 is 10605.
