Least Common Multiple of 105 and 111
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 111 the smallest integer that is 3885 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 111 is 3885.
LCM(105,111) = 3885
LCM of 105 and 111
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 111 by Prime method
- Least Common Multiple of 105 and 111 with GCF Formula
LCM of 105 and 111 is 3885
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 111. First we will calculate the prime factors of 105 and 111.
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 111
| 3 | 111 |
| 37 | 37 |
| 1 |
Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:
111 = 31×371
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 111.
LCM(105,111) = 31×51×71×371
LCM(105,111) = 3885
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 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Least Common Multiple of 105 and 111 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 111, than apply into the LCM equation.
GCF(105,111) = 3
LCM(105,111) = ( 105 × 111) / 3
LCM(105,111) = 11655 / 3
LCM(105,111) = 3885
Properties of LCM 105 and 111
(i) The LCM of 111 and 105 is associative
LCM of 105 and 111 = LCM of 111 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 111
Frequently Asked Questions on LCM of 105 and 111
1. What is the LCM of 105 and 111?
Answer: LCM of 105 and 111 is 3885.
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 111?
Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.
4. How to Find the LCM of 105 and 111?
Answer:
Least Common Multiple of 105 and 111 = 3885
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 111
111 = 3 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3885 = 3 x 5 x 7 x 37
Step 4: Therefore, the least common multiple of 105 and 111 is 3885.