Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6970 and 6972 the smallest integer that is 24297420 that is divisible by both numbers.
Least Common Multiple (LCM) of 6970 and 6972 is 24297420.
LCM(6970,6972) = 24297420
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 6970 and 6972. First we will calculate the prime factors of 6970 and 6972.
Prime Factorization of 6970
2 | 6970 |
5 | 3485 |
17 | 697 |
41 | 41 |
1 |
Prime factors of 6970 are 2, 5, 17,41. Prime factorization of 6970 in exponential form is:
6970 = 21×51×171×411
Prime Factorization of 6972
2 | 6972 |
2 | 3486 |
3 | 1743 |
7 | 581 |
83 | 83 |
1 |
Prime factors of 6972 are 2, 3, 7,83. Prime factorization of 6972 in exponential form is:
6972 = 22×31×71×831
Now multiplying the highest exponent prime factors to calculate the LCM of 6970 and 6972.
LCM(6970,6972) = 22×31×51×71×171×411×831
LCM(6970,6972) = 24297420
Factors of 6970
List of positive integer factors of 6970 that divides 6970 without a remainder.
1, 2, 5, 10, 17, 34, 41, 82, 85, 170, 205, 410, 697, 1394, 3485, 6970
Factors of 6972
List of positive integer factors of 6972 that divides 6972 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 83, 84, 166, 249, 332, 498, 581, 996, 1162, 1743, 2324, 3486, 6972
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6970 and 6972, than apply into the LCM equation.
GCF(6970,6972) = 2
LCM(6970,6972) = ( 6970 × 6972) / 2
LCM(6970,6972) = 48594840 / 2
LCM(6970,6972) = 24297420
(i) The LCM of 6972 and 6970 is associative
LCM of 6970 and 6972 = LCM of 6972 and 6970
1. What is the LCM of 6970 and 6972?
Answer: LCM of 6970 and 6972 is 24297420.
2. What are the Factors of 6970?
Answer: Factors of 6970 are 1, 2, 5, 10, 17, 34, 41, 82, 85, 170, 205, 410, 697, 1394, 3485, 6970. There are 16 integers that are factors of 6970. The greatest factor of 6970 is 6970.
3. What are the Factors of 6972?
Answer: Factors of 6972 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 83, 84, 166, 249, 332, 498, 581, 996, 1162, 1743, 2324, 3486, 6972. There are 24 integers that are factors of 6972. The greatest factor of 6972 is 6972.
4. How to Find the LCM of 6970 and 6972?
Answer:
Least Common Multiple of 6970 and 6972 = 24297420
Step 1: Find the prime factorization of 6970
6970 = 2 x 5 x 17 x 41
Step 2: Find the prime factorization of 6972
6972 = 2 x 2 x 3 x 7 x 83
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 24297420 = 2 x 2 x 3 x 5 x 7 x 17 x 41 x 83
Step 4: Therefore, the least common multiple of 6970 and 6972 is 24297420.