Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 118 and 121 the smallest integer that is 14278 that is divisible by both numbers.
Least Common Multiple (LCM) of 118 and 121 is 14278.
LCM(118,121) = 14278
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 118 and 121. First we will calculate the prime factors of 118 and 121.
Prime Factorization of 118
2 | 118 |
59 | 59 |
1 |
Prime factors of 118 are 2,59. Prime factorization of 118 in exponential form is:
118 = 21×591
Prime Factorization of 121
11 | 121 |
11 | 11 |
1 |
Prime factors of 121 are 11. Prime factorization of 121 in exponential form is:
121 = 112
Now multiplying the highest exponent prime factors to calculate the LCM of 118 and 121.
LCM(118,121) = 21×112×591
LCM(118,121) = 14278
Factors of 118
List of positive integer factors of 118 that divides 118 without a remainder.
1, 2, 59, 118
Factors of 121
List of positive integer factors of 121 that divides 121 without a remainder.
1, 11, 121
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 118 and 121, than apply into the LCM equation.
GCF(118,121) = 1
LCM(118,121) = ( 118 × 121) / 1
LCM(118,121) = 14278 / 1
LCM(118,121) = 14278
(i) The LCM of 121 and 118 is associative
LCM of 118 and 121 = LCM of 121 and 118
1. What is the LCM of 118 and 121?
Answer: LCM of 118 and 121 is 14278.
2. What are the Factors of 118?
Answer: Factors of 118 are 1, 2, 59, 118. There are 4 integers that are factors of 118. The greatest factor of 118 is 118.
3. What are the Factors of 121?
Answer: Factors of 121 are 1, 11, 121. There are 3 integers that are factors of 121. The greatest factor of 121 is 121.
4. How to Find the LCM of 118 and 121?
Answer:
Least Common Multiple of 118 and 121 = 14278
Step 1: Find the prime factorization of 118
118 = 2 x 59
Step 2: Find the prime factorization of 121
121 = 11 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14278 = 2 x 11 x 11 x 59
Step 4: Therefore, the least common multiple of 118 and 121 is 14278.