Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3538 and 3542 the smallest integer that is 6265798 that is divisible by both numbers.
Least Common Multiple (LCM) of 3538 and 3542 is 6265798.
LCM(3538,3542) = 6265798
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 3538 and 3542. First we will calculate the prime factors of 3538 and 3542.
Prime Factorization of 3538
2 | 3538 |
29 | 1769 |
61 | 61 |
1 |
Prime factors of 3538 are 2, 29,61. Prime factorization of 3538 in exponential form is:
3538 = 21×291×611
Prime Factorization of 3542
2 | 3542 |
7 | 1771 |
11 | 253 |
23 | 23 |
1 |
Prime factors of 3542 are 2, 7, 11,23. Prime factorization of 3542 in exponential form is:
3542 = 21×71×111×231
Now multiplying the highest exponent prime factors to calculate the LCM of 3538 and 3542.
LCM(3538,3542) = 21×71×111×231×291×611
LCM(3538,3542) = 6265798
Factors of 3538
List of positive integer factors of 3538 that divides 3538 without a remainder.
1, 2, 29, 58, 61, 122, 1769, 3538
Factors of 3542
List of positive integer factors of 3542 that divides 3542 without a remainder.
1, 2, 7, 11, 14, 22, 23, 46, 77, 154, 161, 253, 322, 506, 1771, 3542
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3538 and 3542, than apply into the LCM equation.
GCF(3538,3542) = 2
LCM(3538,3542) = ( 3538 × 3542) / 2
LCM(3538,3542) = 12531596 / 2
LCM(3538,3542) = 6265798
(i) The LCM of 3542 and 3538 is associative
LCM of 3538 and 3542 = LCM of 3542 and 3538
1. What is the LCM of 3538 and 3542?
Answer: LCM of 3538 and 3542 is 6265798.
2. What are the Factors of 3538?
Answer: Factors of 3538 are 1, 2, 29, 58, 61, 122, 1769, 3538. There are 8 integers that are factors of 3538. The greatest factor of 3538 is 3538.
3. What are the Factors of 3542?
Answer: Factors of 3542 are 1, 2, 7, 11, 14, 22, 23, 46, 77, 154, 161, 253, 322, 506, 1771, 3542. There are 16 integers that are factors of 3542. The greatest factor of 3542 is 3542.
4. How to Find the LCM of 3538 and 3542?
Answer:
Least Common Multiple of 3538 and 3542 = 6265798
Step 1: Find the prime factorization of 3538
3538 = 2 x 29 x 61
Step 2: Find the prime factorization of 3542
3542 = 2 x 7 x 11 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6265798 = 2 x 7 x 11 x 23 x 29 x 61
Step 4: Therefore, the least common multiple of 3538 and 3542 is 6265798.