Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2972 and 2976 the smallest integer that is 2211168 that is divisible by both numbers.
Least Common Multiple (LCM) of 2972 and 2976 is 2211168.
LCM(2972,2976) = 2211168
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 2972 and 2976. First we will calculate the prime factors of 2972 and 2976.
Prime Factorization of 2972
2 | 2972 |
2 | 1486 |
743 | 743 |
1 |
Prime factors of 2972 are 2,743. Prime factorization of 2972 in exponential form is:
2972 = 22×7431
Prime Factorization of 2976
2 | 2976 |
2 | 1488 |
2 | 744 |
2 | 372 |
2 | 186 |
3 | 93 |
31 | 31 |
1 |
Prime factors of 2976 are 2, 3,31. Prime factorization of 2976 in exponential form is:
2976 = 25×31×311
Now multiplying the highest exponent prime factors to calculate the LCM of 2972 and 2976.
LCM(2972,2976) = 25×31×311×7431
LCM(2972,2976) = 2211168
Factors of 2972
List of positive integer factors of 2972 that divides 2972 without a remainder.
1, 2, 4, 743, 1486, 2972
Factors of 2976
List of positive integer factors of 2976 that divides 2976 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 32, 48, 62, 93, 96, 124, 186, 248, 372, 496, 744, 992, 1488, 2976
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2972 and 2976, than apply into the LCM equation.
GCF(2972,2976) = 4
LCM(2972,2976) = ( 2972 × 2976) / 4
LCM(2972,2976) = 8844672 / 4
LCM(2972,2976) = 2211168
(i) The LCM of 2976 and 2972 is associative
LCM of 2972 and 2976 = LCM of 2976 and 2972
1. What is the LCM of 2972 and 2976?
Answer: LCM of 2972 and 2976 is 2211168.
2. What are the Factors of 2972?
Answer: Factors of 2972 are 1, 2, 4, 743, 1486, 2972. There are 6 integers that are factors of 2972. The greatest factor of 2972 is 2972.
3. What are the Factors of 2976?
Answer: Factors of 2976 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 32, 48, 62, 93, 96, 124, 186, 248, 372, 496, 744, 992, 1488, 2976. There are 24 integers that are factors of 2976. The greatest factor of 2976 is 2976.
4. How to Find the LCM of 2972 and 2976?
Answer:
Least Common Multiple of 2972 and 2976 = 2211168
Step 1: Find the prime factorization of 2972
2972 = 2 x 2 x 743
Step 2: Find the prime factorization of 2976
2976 = 2 x 2 x 2 x 2 x 2 x 3 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2211168 = 2 x 2 x 2 x 2 x 2 x 3 x 31 x 743
Step 4: Therefore, the least common multiple of 2972 and 2976 is 2211168.