Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1344 and 1348 the smallest integer that is 452928 that is divisible by both numbers.
Least Common Multiple (LCM) of 1344 and 1348 is 452928.
LCM(1344,1348) = 452928
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 1344 and 1348. First we will calculate the prime factors of 1344 and 1348.
Prime Factorization of 1344
2 | 1344 |
2 | 672 |
2 | 336 |
2 | 168 |
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 1344 are 2, 3,7. Prime factorization of 1344 in exponential form is:
1344 = 26×31×71
Prime Factorization of 1348
2 | 1348 |
2 | 674 |
337 | 337 |
1 |
Prime factors of 1348 are 2,337. Prime factorization of 1348 in exponential form is:
1348 = 22×3371
Now multiplying the highest exponent prime factors to calculate the LCM of 1344 and 1348.
LCM(1344,1348) = 26×31×71×3371
LCM(1344,1348) = 452928
Factors of 1344
List of positive integer factors of 1344 that divides 1344 without a remainder.
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 168, 192, 224, 336, 448, 672, 1344
Factors of 1348
List of positive integer factors of 1348 that divides 1348 without a remainder.
1, 2, 4, 337, 674, 1348
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1344 and 1348, than apply into the LCM equation.
GCF(1344,1348) = 4
LCM(1344,1348) = ( 1344 × 1348) / 4
LCM(1344,1348) = 1811712 / 4
LCM(1344,1348) = 452928
(i) The LCM of 1348 and 1344 is associative
LCM of 1344 and 1348 = LCM of 1348 and 1344
1. What is the LCM of 1344 and 1348?
Answer: LCM of 1344 and 1348 is 452928.
2. What are the Factors of 1344?
Answer: Factors of 1344 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 168, 192, 224, 336, 448, 672, 1344. There are 28 integers that are factors of 1344. The greatest factor of 1344 is 1344.
3. What are the Factors of 1348?
Answer: Factors of 1348 are 1, 2, 4, 337, 674, 1348. There are 6 integers that are factors of 1348. The greatest factor of 1348 is 1348.
4. How to Find the LCM of 1344 and 1348?
Answer:
Least Common Multiple of 1344 and 1348 = 452928
Step 1: Find the prime factorization of 1344
1344 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 1348
1348 = 2 x 2 x 337
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 452928 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 337
Step 4: Therefore, the least common multiple of 1344 and 1348 is 452928.