Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7208 and 7213 the smallest integer that is 51991304 that is divisible by both numbers.
Least Common Multiple (LCM) of 7208 and 7213 is 51991304.
LCM(7208,7213) = 51991304
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 7208 and 7213. First we will calculate the prime factors of 7208 and 7213.
Prime Factorization of 7208
2 | 7208 |
2 | 3604 |
2 | 1802 |
17 | 901 |
53 | 53 |
1 |
Prime factors of 7208 are 2, 17,53. Prime factorization of 7208 in exponential form is:
7208 = 23×171×531
Prime Factorization of 7213
7213 | 7213 |
1 |
Prime factors of 7213 are 7213. Prime factorization of 7213 in exponential form is:
7213 = 72131
Now multiplying the highest exponent prime factors to calculate the LCM of 7208 and 7213.
LCM(7208,7213) = 23×171×531×72131
LCM(7208,7213) = 51991304
Factors of 7208
List of positive integer factors of 7208 that divides 7208 without a remainder.
1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208
Factors of 7213
List of positive integer factors of 7213 that divides 7213 without a remainder.
1, 7213
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7208 and 7213, than apply into the LCM equation.
GCF(7208,7213) = 1
LCM(7208,7213) = ( 7208 × 7213) / 1
LCM(7208,7213) = 51991304 / 1
LCM(7208,7213) = 51991304
(i) The LCM of 7213 and 7208 is associative
LCM of 7208 and 7213 = LCM of 7213 and 7208
1. What is the LCM of 7208 and 7213?
Answer: LCM of 7208 and 7213 is 51991304.
2. What are the Factors of 7208?
Answer: Factors of 7208 are 1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208. There are 16 integers that are factors of 7208. The greatest factor of 7208 is 7208.
3. What are the Factors of 7213?
Answer: Factors of 7213 are 1, 7213. There are 2 integers that are factors of 7213. The greatest factor of 7213 is 7213.
4. How to Find the LCM of 7208 and 7213?
Answer:
Least Common Multiple of 7208 and 7213 = 51991304
Step 1: Find the prime factorization of 7208
7208 = 2 x 2 x 2 x 17 x 53
Step 2: Find the prime factorization of 7213
7213 = 7213
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 51991304 = 2 x 2 x 2 x 17 x 53 x 7213
Step 4: Therefore, the least common multiple of 7208 and 7213 is 51991304.