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 3546 the smallest integer that is 6272874 that is divisible by both numbers.
Least Common Multiple (LCM) of 3538 and 3546 is 6272874.
LCM(3538,3546) = 6272874
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 3546. First we will calculate the prime factors of 3538 and 3546.
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 3546
2 | 3546 |
3 | 1773 |
3 | 591 |
197 | 197 |
1 |
Prime factors of 3546 are 2, 3,197. Prime factorization of 3546 in exponential form is:
3546 = 21×32×1971
Now multiplying the highest exponent prime factors to calculate the LCM of 3538 and 3546.
LCM(3538,3546) = 21×32×291×611×1971
LCM(3538,3546) = 6272874
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 3546
List of positive integer factors of 3546 that divides 3546 without a remainder.
1, 2, 3, 6, 9, 18, 197, 394, 591, 1182, 1773, 3546
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3538 and 3546, than apply into the LCM equation.
GCF(3538,3546) = 2
LCM(3538,3546) = ( 3538 × 3546) / 2
LCM(3538,3546) = 12545748 / 2
LCM(3538,3546) = 6272874
(i) The LCM of 3546 and 3538 is associative
LCM of 3538 and 3546 = LCM of 3546 and 3538
1. What is the LCM of 3538 and 3546?
Answer: LCM of 3538 and 3546 is 6272874.
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 3546?
Answer: Factors of 3546 are 1, 2, 3, 6, 9, 18, 197, 394, 591, 1182, 1773, 3546. There are 12 integers that are factors of 3546. The greatest factor of 3546 is 3546.
4. How to Find the LCM of 3538 and 3546?
Answer:
Least Common Multiple of 3538 and 3546 = 6272874
Step 1: Find the prime factorization of 3538
3538 = 2 x 29 x 61
Step 2: Find the prime factorization of 3546
3546 = 2 x 3 x 3 x 197
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6272874 = 2 x 3 x 3 x 29 x 61 x 197
Step 4: Therefore, the least common multiple of 3538 and 3546 is 6272874.