Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 393 and 396 the smallest integer that is 51876 that is divisible by both numbers.
Least Common Multiple (LCM) of 393 and 396 is 51876.
LCM(393,396) = 51876
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 393 and 396. First we will calculate the prime factors of 393 and 396.
Prime Factorization of 393
3 | 393 |
131 | 131 |
1 |
Prime factors of 393 are 3,131. Prime factorization of 393 in exponential form is:
393 = 31×1311
Prime Factorization of 396
2 | 396 |
2 | 198 |
3 | 99 |
3 | 33 |
11 | 11 |
1 |
Prime factors of 396 are 2, 3,11. Prime factorization of 396 in exponential form is:
396 = 22×32×111
Now multiplying the highest exponent prime factors to calculate the LCM of 393 and 396.
LCM(393,396) = 22×32×111×1311
LCM(393,396) = 51876
Factors of 393
List of positive integer factors of 393 that divides 393 without a remainder.
1, 3, 131, 393
Factors of 396
List of positive integer factors of 396 that divides 396 without a remainder.
1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 393 and 396, than apply into the LCM equation.
GCF(393,396) = 3
LCM(393,396) = ( 393 × 396) / 3
LCM(393,396) = 155628 / 3
LCM(393,396) = 51876
(i) The LCM of 396 and 393 is associative
LCM of 393 and 396 = LCM of 396 and 393
1. What is the LCM of 393 and 396?
Answer: LCM of 393 and 396 is 51876.
2. What are the Factors of 393?
Answer: Factors of 393 are 1, 3, 131, 393. There are 4 integers that are factors of 393. The greatest factor of 393 is 393.
3. What are the Factors of 396?
Answer: Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396. There are 18 integers that are factors of 396. The greatest factor of 396 is 396.
4. How to Find the LCM of 393 and 396?
Answer:
Least Common Multiple of 393 and 396 = 51876
Step 1: Find the prime factorization of 393
393 = 3 x 131
Step 2: Find the prime factorization of 396
396 = 2 x 2 x 3 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 = 51876 = 2 x 2 x 3 x 3 x 11 x 131
Step 4: Therefore, the least common multiple of 393 and 396 is 51876.