Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5352 and 5360 the smallest integer that is 3585840 that is divisible by both numbers.
Least Common Multiple (LCM) of 5352 and 5360 is 3585840.
LCM(5352,5360) = 3585840
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 5352 and 5360. First we will calculate the prime factors of 5352 and 5360.
Prime Factorization of 5352
2 | 5352 |
2 | 2676 |
2 | 1338 |
3 | 669 |
223 | 223 |
1 |
Prime factors of 5352 are 2, 3,223. Prime factorization of 5352 in exponential form is:
5352 = 23×31×2231
Prime Factorization of 5360
2 | 5360 |
2 | 2680 |
2 | 1340 |
2 | 670 |
5 | 335 |
67 | 67 |
1 |
Prime factors of 5360 are 2, 5,67. Prime factorization of 5360 in exponential form is:
5360 = 24×51×671
Now multiplying the highest exponent prime factors to calculate the LCM of 5352 and 5360.
LCM(5352,5360) = 24×31×51×671×2231
LCM(5352,5360) = 3585840
Factors of 5352
List of positive integer factors of 5352 that divides 5352 without a remainder.
1, 2, 3, 4, 6, 8, 12, 24, 223, 446, 669, 892, 1338, 1784, 2676, 5352
Factors of 5360
List of positive integer factors of 5360 that divides 5360 without a remainder.
1, 2, 4, 5, 8, 10, 16, 20, 40, 67, 80, 134, 268, 335, 536, 670, 1072, 1340, 2680, 5360
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5352 and 5360, than apply into the LCM equation.
GCF(5352,5360) = 8
LCM(5352,5360) = ( 5352 × 5360) / 8
LCM(5352,5360) = 28686720 / 8
LCM(5352,5360) = 3585840
(i) The LCM of 5360 and 5352 is associative
LCM of 5352 and 5360 = LCM of 5360 and 5352
1. What is the LCM of 5352 and 5360?
Answer: LCM of 5352 and 5360 is 3585840.
2. What are the Factors of 5352?
Answer: Factors of 5352 are 1, 2, 3, 4, 6, 8, 12, 24, 223, 446, 669, 892, 1338, 1784, 2676, 5352. There are 16 integers that are factors of 5352. The greatest factor of 5352 is 5352.
3. What are the Factors of 5360?
Answer: Factors of 5360 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 67, 80, 134, 268, 335, 536, 670, 1072, 1340, 2680, 5360. There are 20 integers that are factors of 5360. The greatest factor of 5360 is 5360.
4. How to Find the LCM of 5352 and 5360?
Answer:
Least Common Multiple of 5352 and 5360 = 3585840
Step 1: Find the prime factorization of 5352
5352 = 2 x 2 x 2 x 3 x 223
Step 2: Find the prime factorization of 5360
5360 = 2 x 2 x 2 x 2 x 5 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3585840 = 2 x 2 x 2 x 2 x 3 x 5 x 67 x 223
Step 4: Therefore, the least common multiple of 5352 and 5360 is 3585840.