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 7216 the smallest integer that is 6501616 that is divisible by both numbers.
Least Common Multiple (LCM) of 7208 and 7216 is 6501616.
LCM(7208,7216) = 6501616
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 7216. First we will calculate the prime factors of 7208 and 7216.
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 7216
2 | 7216 |
2 | 3608 |
2 | 1804 |
2 | 902 |
11 | 451 |
41 | 41 |
1 |
Prime factors of 7216 are 2, 11,41. Prime factorization of 7216 in exponential form is:
7216 = 24×111×411
Now multiplying the highest exponent prime factors to calculate the LCM of 7208 and 7216.
LCM(7208,7216) = 24×111×171×411×531
LCM(7208,7216) = 6501616
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 7216
List of positive integer factors of 7216 that divides 7216 without a remainder.
1, 2, 4, 8, 11, 16, 22, 41, 44, 82, 88, 164, 176, 328, 451, 656, 902, 1804, 3608, 7216
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7208 and 7216, than apply into the LCM equation.
GCF(7208,7216) = 8
LCM(7208,7216) = ( 7208 × 7216) / 8
LCM(7208,7216) = 52012928 / 8
LCM(7208,7216) = 6501616
(i) The LCM of 7216 and 7208 is associative
LCM of 7208 and 7216 = LCM of 7216 and 7208
1. What is the LCM of 7208 and 7216?
Answer: LCM of 7208 and 7216 is 6501616.
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 7216?
Answer: Factors of 7216 are 1, 2, 4, 8, 11, 16, 22, 41, 44, 82, 88, 164, 176, 328, 451, 656, 902, 1804, 3608, 7216. There are 20 integers that are factors of 7216. The greatest factor of 7216 is 7216.
4. How to Find the LCM of 7208 and 7216?
Answer:
Least Common Multiple of 7208 and 7216 = 6501616
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 7216
7216 = 2 x 2 x 2 x 2 x 11 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6501616 = 2 x 2 x 2 x 2 x 11 x 17 x 41 x 53
Step 4: Therefore, the least common multiple of 7208 and 7216 is 6501616.