Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1356 and 1360 the smallest integer that is 461040 that is divisible by both numbers.
Least Common Multiple (LCM) of 1356 and 1360 is 461040.
LCM(1356,1360) = 461040
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 1356 and 1360. First we will calculate the prime factors of 1356 and 1360.
Prime Factorization of 1356
2 | 1356 |
2 | 678 |
3 | 339 |
113 | 113 |
1 |
Prime factors of 1356 are 2, 3,113. Prime factorization of 1356 in exponential form is:
1356 = 22×31×1131
Prime Factorization of 1360
2 | 1360 |
2 | 680 |
2 | 340 |
2 | 170 |
5 | 85 |
17 | 17 |
1 |
Prime factors of 1360 are 2, 5,17. Prime factorization of 1360 in exponential form is:
1360 = 24×51×171
Now multiplying the highest exponent prime factors to calculate the LCM of 1356 and 1360.
LCM(1356,1360) = 24×31×51×171×1131
LCM(1356,1360) = 461040
Factors of 1356
List of positive integer factors of 1356 that divides 1356 without a remainder.
1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356
Factors of 1360
List of positive integer factors of 1360 that divides 1360 without a remainder.
1, 2, 4, 5, 8, 10, 16, 17, 20, 34, 40, 68, 80, 85, 136, 170, 272, 340, 680, 1360
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1356 and 1360, than apply into the LCM equation.
GCF(1356,1360) = 4
LCM(1356,1360) = ( 1356 × 1360) / 4
LCM(1356,1360) = 1844160 / 4
LCM(1356,1360) = 461040
(i) The LCM of 1360 and 1356 is associative
LCM of 1356 and 1360 = LCM of 1360 and 1356
1. What is the LCM of 1356 and 1360?
Answer: LCM of 1356 and 1360 is 461040.
2. What are the Factors of 1356?
Answer: Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356. There are 12 integers that are factors of 1356. The greatest factor of 1356 is 1356.
3. What are the Factors of 1360?
Answer: Factors of 1360 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 34, 40, 68, 80, 85, 136, 170, 272, 340, 680, 1360. There are 20 integers that are factors of 1360. The greatest factor of 1360 is 1360.
4. How to Find the LCM of 1356 and 1360?
Answer:
Least Common Multiple of 1356 and 1360 = 461040
Step 1: Find the prime factorization of 1356
1356 = 2 x 2 x 3 x 113
Step 2: Find the prime factorization of 1360
1360 = 2 x 2 x 2 x 2 x 5 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 461040 = 2 x 2 x 2 x 2 x 3 x 5 x 17 x 113
Step 4: Therefore, the least common multiple of 1356 and 1360 is 461040.