Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1368 and 1372 the smallest integer that is 469224 that is divisible by both numbers.
Least Common Multiple (LCM) of 1368 and 1372 is 469224.
LCM(1368,1372) = 469224
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 1368 and 1372. First we will calculate the prime factors of 1368 and 1372.
Prime Factorization of 1368
2 | 1368 |
2 | 684 |
2 | 342 |
3 | 171 |
3 | 57 |
19 | 19 |
1 |
Prime factors of 1368 are 2, 3,19. Prime factorization of 1368 in exponential form is:
1368 = 23×32×191
Prime Factorization of 1372
2 | 1372 |
2 | 686 |
7 | 343 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 1372 are 2,7. Prime factorization of 1372 in exponential form is:
1372 = 22×73
Now multiplying the highest exponent prime factors to calculate the LCM of 1368 and 1372.
LCM(1368,1372) = 23×32×73×191
LCM(1368,1372) = 469224
Factors of 1368
List of positive integer factors of 1368 that divides 1368 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 456, 684, 1368
Factors of 1372
List of positive integer factors of 1372 that divides 1372 without a remainder.
1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1368 and 1372, than apply into the LCM equation.
GCF(1368,1372) = 4
LCM(1368,1372) = ( 1368 × 1372) / 4
LCM(1368,1372) = 1876896 / 4
LCM(1368,1372) = 469224
(i) The LCM of 1372 and 1368 is associative
LCM of 1368 and 1372 = LCM of 1372 and 1368
1. What is the LCM of 1368 and 1372?
Answer: LCM of 1368 and 1372 is 469224.
2. What are the Factors of 1368?
Answer: Factors of 1368 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 456, 684, 1368. There are 24 integers that are factors of 1368. The greatest factor of 1368 is 1368.
3. What are the Factors of 1372?
Answer: Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372. There are 12 integers that are factors of 1372. The greatest factor of 1372 is 1372.
4. How to Find the LCM of 1368 and 1372?
Answer:
Least Common Multiple of 1368 and 1372 = 469224
Step 1: Find the prime factorization of 1368
1368 = 2 x 2 x 2 x 3 x 3 x 19
Step 2: Find the prime factorization of 1372
1372 = 2 x 2 x 7 x 7 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 469224 = 2 x 2 x 2 x 3 x 3 x 7 x 7 x 7 x 19
Step 4: Therefore, the least common multiple of 1368 and 1372 is 469224.