Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6965 and 6972 the smallest integer that is 6937140 that is divisible by both numbers.
Least Common Multiple (LCM) of 6965 and 6972 is 6937140.
LCM(6965,6972) = 6937140
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 6965 and 6972. First we will calculate the prime factors of 6965 and 6972.
Prime Factorization of 6965
5 | 6965 |
7 | 1393 |
199 | 199 |
1 |
Prime factors of 6965 are 5, 7,199. Prime factorization of 6965 in exponential form is:
6965 = 51×71×1991
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 6965 and 6972.
LCM(6965,6972) = 22×31×51×71×831×1991
LCM(6965,6972) = 6937140
Factors of 6965
List of positive integer factors of 6965 that divides 6965 without a remainder.
1, 5, 7, 35, 199, 995, 1393, 6965
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 6965 and 6972, than apply into the LCM equation.
GCF(6965,6972) = 7
LCM(6965,6972) = ( 6965 × 6972) / 7
LCM(6965,6972) = 48559980 / 7
LCM(6965,6972) = 6937140
(i) The LCM of 6972 and 6965 is associative
LCM of 6965 and 6972 = LCM of 6972 and 6965
1. What is the LCM of 6965 and 6972?
Answer: LCM of 6965 and 6972 is 6937140.
2. What are the Factors of 6965?
Answer: Factors of 6965 are 1, 5, 7, 35, 199, 995, 1393, 6965. There are 8 integers that are factors of 6965. The greatest factor of 6965 is 6965.
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 6965 and 6972?
Answer:
Least Common Multiple of 6965 and 6972 = 6937140
Step 1: Find the prime factorization of 6965
6965 = 5 x 7 x 199
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 = 6937140 = 2 x 2 x 3 x 5 x 7 x 83 x 199
Step 4: Therefore, the least common multiple of 6965 and 6972 is 6937140.