Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2344 and 2352 the smallest integer that is 689136 that is divisible by both numbers.
Least Common Multiple (LCM) of 2344 and 2352 is 689136.
LCM(2344,2352) = 689136
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 2344 and 2352. First we will calculate the prime factors of 2344 and 2352.
Prime Factorization of 2344
2 | 2344 |
2 | 1172 |
2 | 586 |
293 | 293 |
1 |
Prime factors of 2344 are 2,293. Prime factorization of 2344 in exponential form is:
2344 = 23×2931
Prime Factorization of 2352
2 | 2352 |
2 | 1176 |
2 | 588 |
2 | 294 |
3 | 147 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 2352 are 2, 3,7. Prime factorization of 2352 in exponential form is:
2352 = 24×31×72
Now multiplying the highest exponent prime factors to calculate the LCM of 2344 and 2352.
LCM(2344,2352) = 24×31×72×2931
LCM(2344,2352) = 689136
Factors of 2344
List of positive integer factors of 2344 that divides 2344 without a remainder.
1, 2, 4, 8, 293, 586, 1172, 2344
Factors of 2352
List of positive integer factors of 2352 that divides 2352 without a remainder.
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2344 and 2352, than apply into the LCM equation.
GCF(2344,2352) = 8
LCM(2344,2352) = ( 2344 × 2352) / 8
LCM(2344,2352) = 5513088 / 8
LCM(2344,2352) = 689136
(i) The LCM of 2352 and 2344 is associative
LCM of 2344 and 2352 = LCM of 2352 and 2344
1. What is the LCM of 2344 and 2352?
Answer: LCM of 2344 and 2352 is 689136.
2. What are the Factors of 2344?
Answer: Factors of 2344 are 1, 2, 4, 8, 293, 586, 1172, 2344. There are 8 integers that are factors of 2344. The greatest factor of 2344 is 2344.
3. What are the Factors of 2352?
Answer: Factors of 2352 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352. There are 30 integers that are factors of 2352. The greatest factor of 2352 is 2352.
4. How to Find the LCM of 2344 and 2352?
Answer:
Least Common Multiple of 2344 and 2352 = 689136
Step 1: Find the prime factorization of 2344
2344 = 2 x 2 x 2 x 293
Step 2: Find the prime factorization of 2352
2352 = 2 x 2 x 2 x 2 x 3 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 = 689136 = 2 x 2 x 2 x 2 x 3 x 7 x 7 x 293
Step 4: Therefore, the least common multiple of 2344 and 2352 is 689136.