Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2698 and 2704 the smallest integer that is 3647696 that is divisible by both numbers.
Least Common Multiple (LCM) of 2698 and 2704 is 3647696.
LCM(2698,2704) = 3647696
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 2698 and 2704. First we will calculate the prime factors of 2698 and 2704.
Prime Factorization of 2698
2 | 2698 |
19 | 1349 |
71 | 71 |
1 |
Prime factors of 2698 are 2, 19,71. Prime factorization of 2698 in exponential form is:
2698 = 21×191×711
Prime Factorization of 2704
2 | 2704 |
2 | 1352 |
2 | 676 |
2 | 338 |
13 | 169 |
13 | 13 |
1 |
Prime factors of 2704 are 2,13. Prime factorization of 2704 in exponential form is:
2704 = 24×132
Now multiplying the highest exponent prime factors to calculate the LCM of 2698 and 2704.
LCM(2698,2704) = 24×132×191×711
LCM(2698,2704) = 3647696
Factors of 2698
List of positive integer factors of 2698 that divides 2698 without a remainder.
1, 2, 19, 38, 71, 142, 1349, 2698
Factors of 2704
List of positive integer factors of 2704 that divides 2704 without a remainder.
1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2698 and 2704, than apply into the LCM equation.
GCF(2698,2704) = 2
LCM(2698,2704) = ( 2698 × 2704) / 2
LCM(2698,2704) = 7295392 / 2
LCM(2698,2704) = 3647696
(i) The LCM of 2704 and 2698 is associative
LCM of 2698 and 2704 = LCM of 2704 and 2698
1. What is the LCM of 2698 and 2704?
Answer: LCM of 2698 and 2704 is 3647696.
2. What are the Factors of 2698?
Answer: Factors of 2698 are 1, 2, 19, 38, 71, 142, 1349, 2698. There are 8 integers that are factors of 2698. The greatest factor of 2698 is 2698.
3. What are the Factors of 2704?
Answer: Factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704. There are 15 integers that are factors of 2704. The greatest factor of 2704 is 2704.
4. How to Find the LCM of 2698 and 2704?
Answer:
Least Common Multiple of 2698 and 2704 = 3647696
Step 1: Find the prime factorization of 2698
2698 = 2 x 19 x 71
Step 2: Find the prime factorization of 2704
2704 = 2 x 2 x 2 x 2 x 13 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3647696 = 2 x 2 x 2 x 2 x 13 x 13 x 19 x 71
Step 4: Therefore, the least common multiple of 2698 and 2704 is 3647696.