Least Common Multiple of 112 and 119
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 112 and 119 the smallest integer that is 1904 that is divisible by both numbers.
Least Common Multiple (LCM) of 112 and 119 is 1904.
LCM(112,119) = 1904
LCM of 112 and 119
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 112 and 119 by Prime method
- Least Common Multiple of 112 and 119 with GCF Formula
LCM of 112 and 119 is 1904
Least common multiple can be found by multiplying the highest exponent prime factors of 112 and 119. First we will calculate the prime factors of 112 and 119.
Prime Factorization of 112
| 2 | 112 |
| 2 | 56 |
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:
112 = 24×71
Prime Factorization of 119
| 7 | 119 |
| 17 | 17 |
| 1 |
Prime factors of 119 are 7,17. Prime factorization of 119 in exponential form is:
119 = 71×171
Now multiplying the highest exponent prime factors to calculate the LCM of 112 and 119.
LCM(112,119) = 24×71×171
LCM(112,119) = 1904
Factors of 112
List of positive integer factors of 112 that divides 112 without a remainder.
1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 119
List of positive integer factors of 119 that divides 119 without a remainder.
1, 7, 17, 119
Least Common Multiple of 112 and 119 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 112 and 119, than apply into the LCM equation.
GCF(112,119) = 7
LCM(112,119) = ( 112 × 119) / 7
LCM(112,119) = 13328 / 7
LCM(112,119) = 1904
Properties of LCM 112 and 119
(i) The LCM of 119 and 112 is associative
LCM of 112 and 119 = LCM of 119 and 112
Related Least Common Multiples of 112
Related Least Common Multiples of 119
Frequently Asked Questions on LCM of 112 and 119
1. What is the LCM of 112 and 119?
Answer: LCM of 112 and 119 is 1904.
2. What are the Factors of 112?
Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.
3. What are the Factors of 119?
Answer: Factors of 119 are 1, 7, 17, 119. There are 4 integers that are factors of 119. The greatest factor of 119 is 119.
4. How to Find the LCM of 112 and 119?
Answer:
Least Common Multiple of 112 and 119 = 1904
Step 1: Find the prime factorization of 112
112 = 2 x 2 x 2 x 2 x 7
Step 2: Find the prime factorization of 119
119 = 7 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1904 = 2 x 2 x 2 x 2 x 7 x 17
Step 4: Therefore, the least common multiple of 112 and 119 is 1904.