Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3969 and 3976 the smallest integer that is 2254392 that is divisible by both numbers.
Least Common Multiple (LCM) of 3969 and 3976 is 2254392.
LCM(3969,3976) = 2254392
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 3969 and 3976. First we will calculate the prime factors of 3969 and 3976.
Prime Factorization of 3969
3 | 3969 |
3 | 1323 |
3 | 441 |
3 | 147 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 3969 are 3,7. Prime factorization of 3969 in exponential form is:
3969 = 34×72
Prime Factorization of 3976
2 | 3976 |
2 | 1988 |
2 | 994 |
7 | 497 |
71 | 71 |
1 |
Prime factors of 3976 are 2, 7,71. Prime factorization of 3976 in exponential form is:
3976 = 23×71×711
Now multiplying the highest exponent prime factors to calculate the LCM of 3969 and 3976.
LCM(3969,3976) = 23×34×72×711
LCM(3969,3976) = 2254392
Factors of 3969
List of positive integer factors of 3969 that divides 3969 without a remainder.
1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969
Factors of 3976
List of positive integer factors of 3976 that divides 3976 without a remainder.
1, 2, 4, 7, 8, 14, 28, 56, 71, 142, 284, 497, 568, 994, 1988, 3976
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3969 and 3976, than apply into the LCM equation.
GCF(3969,3976) = 7
LCM(3969,3976) = ( 3969 × 3976) / 7
LCM(3969,3976) = 15780744 / 7
LCM(3969,3976) = 2254392
(i) The LCM of 3976 and 3969 is associative
LCM of 3969 and 3976 = LCM of 3976 and 3969
1. What is the LCM of 3969 and 3976?
Answer: LCM of 3969 and 3976 is 2254392.
2. What are the Factors of 3969?
Answer: Factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969. There are 15 integers that are factors of 3969. The greatest factor of 3969 is 3969.
3. What are the Factors of 3976?
Answer: Factors of 3976 are 1, 2, 4, 7, 8, 14, 28, 56, 71, 142, 284, 497, 568, 994, 1988, 3976. There are 16 integers that are factors of 3976. The greatest factor of 3976 is 3976.
4. How to Find the LCM of 3969 and 3976?
Answer:
Least Common Multiple of 3969 and 3976 = 2254392
Step 1: Find the prime factorization of 3969
3969 = 3 x 3 x 3 x 3 x 7 x 7
Step 2: Find the prime factorization of 3976
3976 = 2 x 2 x 2 x 7 x 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2254392 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7 x 7 x 71
Step 4: Therefore, the least common multiple of 3969 and 3976 is 2254392.