Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 121 and 132 the smallest integer that is 1452 that is divisible by both numbers.
Least Common Multiple (LCM) of 121 and 132 is 1452.
LCM(121,132) = 1452
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 121 and 132. First we will calculate the prime factors of 121 and 132.
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
Prime Factorization of 132
2 | 132 |
2 | 66 |
3 | 33 |
11 | 11 |
1 |
Prime factors of 132 are 2, 3,11. Prime factorization of 132 in exponential form is:
132 = 22×31×111
Now multiplying the highest exponent prime factors to calculate the LCM of 121 and 132.
LCM(121,132) = 22×31×112
LCM(121,132) = 1452
Factors of 121
List of positive integer factors of 121 that divides 121 without a remainder.
1, 11, 121
Factors of 132
List of positive integer factors of 132 that divides 132 without a remainder.
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 121 and 132, than apply into the LCM equation.
GCF(121,132) = 11
LCM(121,132) = ( 121 × 132) / 11
LCM(121,132) = 15972 / 11
LCM(121,132) = 1452
(i) The LCM of 132 and 121 is associative
LCM of 121 and 132 = LCM of 132 and 121
1. What is the LCM of 121 and 132?
Answer: LCM of 121 and 132 is 1452.
2. 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.
3. What are the Factors of 132?
Answer: Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. There are 12 integers that are factors of 132. The greatest factor of 132 is 132.
4. How to Find the LCM of 121 and 132?
Answer:
Least Common Multiple of 121 and 132 = 1452
Step 1: Find the prime factorization of 121
121 = 11 x 11
Step 2: Find the prime factorization of 132
132 = 2 x 2 x 3 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 = 1452 = 2 x 2 x 3 x 11 x 11
Step 4: Therefore, the least common multiple of 121 and 132 is 1452.