Least Common Multiple of 114 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 114 and 119 the smallest integer that is 13566 that is divisible by both numbers.
Least Common Multiple (LCM) of 114 and 119 is 13566.
LCM(114,119) = 13566
LCM of 114 and 119
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 114 and 119 by Prime method
- Least Common Multiple of 114 and 119 with GCF Formula
LCM of 114 and 119 is 13566
Least common multiple can be found by multiplying the highest exponent prime factors of 114 and 119. First we will calculate the prime factors of 114 and 119.
Prime Factorization of 114
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 114 are 2, 3,19. Prime factorization of 114 in exponential form is:
114 = 21×31×191
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 114 and 119.
LCM(114,119) = 21×31×71×171×191
LCM(114,119) = 13566
Factors of 114
List of positive integer factors of 114 that divides 114 without a remainder.
1, 2, 3, 6, 19, 38, 57, 114
Factors of 119
List of positive integer factors of 119 that divides 119 without a remainder.
1, 7, 17, 119
Least Common Multiple of 114 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 114 and 119, than apply into the LCM equation.
GCF(114,119) = 1
LCM(114,119) = ( 114 × 119) / 1
LCM(114,119) = 13566 / 1
LCM(114,119) = 13566
Properties of LCM 114 and 119
(i) The LCM of 119 and 114 is associative
LCM of 114 and 119 = LCM of 119 and 114
Related Least Common Multiples of 114
Related Least Common Multiples of 119
Frequently Asked Questions on LCM of 114 and 119
1. What is the LCM of 114 and 119?
Answer: LCM of 114 and 119 is 13566.
2. What are the Factors of 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
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 114 and 119?
Answer:
Least Common Multiple of 114 and 119 = 13566
Step 1: Find the prime factorization of 114
114 = 2 x 3 x 19
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 = 13566 = 2 x 3 x 7 x 17 x 19
Step 4: Therefore, the least common multiple of 114 and 119 is 13566.