Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 119 and 120 the smallest integer that is 14280 that is divisible by both numbers.
Least Common Multiple (LCM) of 119 and 120 is 14280.
LCM(119,120) = 14280
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 119 and 120. First we will calculate the prime factors of 119 and 120.
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
Prime Factorization of 120
2 | 120 |
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 120 are 2, 3,5. Prime factorization of 120 in exponential form is:
120 = 23×31×51
Now multiplying the highest exponent prime factors to calculate the LCM of 119 and 120.
LCM(119,120) = 23×31×51×71×171
LCM(119,120) = 14280
Factors of 119
List of positive integer factors of 119 that divides 119 without a remainder.
1, 7, 17, 119
Factors of 120
List of positive integer factors of 120 that divides 120 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 119 and 120, than apply into the LCM equation.
GCF(119,120) = 1
LCM(119,120) = ( 119 × 120) / 1
LCM(119,120) = 14280 / 1
LCM(119,120) = 14280
(i) The LCM of 120 and 119 is associative
LCM of 119 and 120 = LCM of 120 and 119
1. What is the LCM of 119 and 120?
Answer: LCM of 119 and 120 is 14280.
2. 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.
3. What are the Factors of 120?
Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.
4. How to Find the LCM of 119 and 120?
Answer:
Least Common Multiple of 119 and 120 = 14280
Step 1: Find the prime factorization of 119
119 = 7 x 17
Step 2: Find the prime factorization of 120
120 = 2 x 2 x 2 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14280 = 2 x 2 x 2 x 3 x 5 x 7 x 17
Step 4: Therefore, the least common multiple of 119 and 120 is 14280.