Least Common Multiple of 104 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 104 and 111 the smallest integer that is 11544 that is divisible by both numbers.
Least Common Multiple (LCM) of 104 and 111 is 11544.
LCM(104,111) = 11544
LCM of 104 and 111
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 104 and 111 by Prime method
- Least Common Multiple of 104 and 111 with GCF Formula
LCM of 104 and 111 is 11544
Least common multiple can be found by multiplying the highest exponent prime factors of 104 and 111. First we will calculate the prime factors of 104 and 111.
Prime Factorization of 104
| 2 | 104 |
| 2 | 52 |
| 2 | 26 |
| 13 | 13 |
| 1 |
Prime factors of 104 are 2,13. Prime factorization of 104 in exponential form is:
104 = 23×131
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 104 and 111.
LCM(104,111) = 23×31×131×371
LCM(104,111) = 11544
Factors of 104
List of positive integer factors of 104 that divides 104 without a remainder.
1, 2, 4, 8, 13, 26, 52, 104
Factors of 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Least Common Multiple of 104 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 104 and 111, than apply into the LCM equation.
GCF(104,111) = 1
LCM(104,111) = ( 104 × 111) / 1
LCM(104,111) = 11544 / 1
LCM(104,111) = 11544
Properties of LCM 104 and 111
(i) The LCM of 111 and 104 is associative
LCM of 104 and 111 = LCM of 111 and 104
Related Least Common Multiples of 104
Related Least Common Multiples of 111
Frequently Asked Questions on LCM of 104 and 111
1. What is the LCM of 104 and 111?
Answer: LCM of 104 and 111 is 11544.
2. What are the Factors of 104?
Answer: Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. There are 8 integers that are factors of 104. The greatest factor of 104 is 104.
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 104 and 111?
Answer:
Least Common Multiple of 104 and 111 = 11544
Step 1: Find the prime factorization of 104
104 = 2 x 2 x 2 x 13
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 = 11544 = 2 x 2 x 2 x 3 x 13 x 37
Step 4: Therefore, the least common multiple of 104 and 111 is 11544.
