Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2349 and 2354 the smallest integer that is 5529546 that is divisible by both numbers.
Least Common Multiple (LCM) of 2349 and 2354 is 5529546.
LCM(2349,2354) = 5529546
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 2349 and 2354. First we will calculate the prime factors of 2349 and 2354.
Prime Factorization of 2349
3 | 2349 |
3 | 783 |
3 | 261 |
3 | 87 |
29 | 29 |
1 |
Prime factors of 2349 are 3,29. Prime factorization of 2349 in exponential form is:
2349 = 34×291
Prime Factorization of 2354
2 | 2354 |
11 | 1177 |
107 | 107 |
1 |
Prime factors of 2354 are 2, 11,107. Prime factorization of 2354 in exponential form is:
2354 = 21×111×1071
Now multiplying the highest exponent prime factors to calculate the LCM of 2349 and 2354.
LCM(2349,2354) = 21×34×111×291×1071
LCM(2349,2354) = 5529546
Factors of 2349
List of positive integer factors of 2349 that divides 2349 without a remainder.
1, 3, 9, 27, 29, 81, 87, 261, 783, 2349
Factors of 2354
List of positive integer factors of 2354 that divides 2354 without a remainder.
1, 2, 11, 22, 107, 214, 1177, 2354
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2349 and 2354, than apply into the LCM equation.
GCF(2349,2354) = 1
LCM(2349,2354) = ( 2349 × 2354) / 1
LCM(2349,2354) = 5529546 / 1
LCM(2349,2354) = 5529546
(i) The LCM of 2354 and 2349 is associative
LCM of 2349 and 2354 = LCM of 2354 and 2349
1. What is the LCM of 2349 and 2354?
Answer: LCM of 2349 and 2354 is 5529546.
2. What are the Factors of 2349?
Answer: Factors of 2349 are 1, 3, 9, 27, 29, 81, 87, 261, 783, 2349. There are 10 integers that are factors of 2349. The greatest factor of 2349 is 2349.
3. What are the Factors of 2354?
Answer: Factors of 2354 are 1, 2, 11, 22, 107, 214, 1177, 2354. There are 8 integers that are factors of 2354. The greatest factor of 2354 is 2354.
4. How to Find the LCM of 2349 and 2354?
Answer:
Least Common Multiple of 2349 and 2354 = 5529546
Step 1: Find the prime factorization of 2349
2349 = 3 x 3 x 3 x 3 x 29
Step 2: Find the prime factorization of 2354
2354 = 2 x 11 x 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5529546 = 2 x 3 x 3 x 3 x 3 x 11 x 29 x 107
Step 4: Therefore, the least common multiple of 2349 and 2354 is 5529546.