Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2346 and 2352 the smallest integer that is 919632 that is divisible by both numbers.
Least Common Multiple (LCM) of 2346 and 2352 is 919632.
LCM(2346,2352) = 919632
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 2346 and 2352. First we will calculate the prime factors of 2346 and 2352.
Prime Factorization of 2346
2 | 2346 |
3 | 1173 |
17 | 391 |
23 | 23 |
1 |
Prime factors of 2346 are 2, 3, 17,23. Prime factorization of 2346 in exponential form is:
2346 = 21×31×171×231
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 2346 and 2352.
LCM(2346,2352) = 24×31×72×171×231
LCM(2346,2352) = 919632
Factors of 2346
List of positive integer factors of 2346 that divides 2346 without a remainder.
1, 2, 3, 6, 17, 23, 34, 46, 51, 69, 102, 138, 391, 782, 1173, 2346
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 2346 and 2352, than apply into the LCM equation.
GCF(2346,2352) = 6
LCM(2346,2352) = ( 2346 × 2352) / 6
LCM(2346,2352) = 5517792 / 6
LCM(2346,2352) = 919632
(i) The LCM of 2352 and 2346 is associative
LCM of 2346 and 2352 = LCM of 2352 and 2346
1. What is the LCM of 2346 and 2352?
Answer: LCM of 2346 and 2352 is 919632.
2. What are the Factors of 2346?
Answer: Factors of 2346 are 1, 2, 3, 6, 17, 23, 34, 46, 51, 69, 102, 138, 391, 782, 1173, 2346. There are 16 integers that are factors of 2346. The greatest factor of 2346 is 2346.
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 2346 and 2352?
Answer:
Least Common Multiple of 2346 and 2352 = 919632
Step 1: Find the prime factorization of 2346
2346 = 2 x 3 x 17 x 23
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 = 919632 = 2 x 2 x 2 x 2 x 3 x 7 x 7 x 17 x 23
Step 4: Therefore, the least common multiple of 2346 and 2352 is 919632.