Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5200 and 5206 the smallest integer that is 13535600 that is divisible by both numbers.
Least Common Multiple (LCM) of 5200 and 5206 is 13535600.
LCM(5200,5206) = 13535600
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 5200 and 5206. First we will calculate the prime factors of 5200 and 5206.
Prime Factorization of 5200
2 | 5200 |
2 | 2600 |
2 | 1300 |
2 | 650 |
5 | 325 |
5 | 65 |
13 | 13 |
1 |
Prime factors of 5200 are 2, 5,13. Prime factorization of 5200 in exponential form is:
5200 = 24×52×131
Prime Factorization of 5206
2 | 5206 |
19 | 2603 |
137 | 137 |
1 |
Prime factors of 5206 are 2, 19,137. Prime factorization of 5206 in exponential form is:
5206 = 21×191×1371
Now multiplying the highest exponent prime factors to calculate the LCM of 5200 and 5206.
LCM(5200,5206) = 24×52×131×191×1371
LCM(5200,5206) = 13535600
Factors of 5200
List of positive integer factors of 5200 that divides 5200 without a remainder.
1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200
Factors of 5206
List of positive integer factors of 5206 that divides 5206 without a remainder.
1, 2, 19, 38, 137, 274, 2603, 5206
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5200 and 5206, than apply into the LCM equation.
GCF(5200,5206) = 2
LCM(5200,5206) = ( 5200 × 5206) / 2
LCM(5200,5206) = 27071200 / 2
LCM(5200,5206) = 13535600
(i) The LCM of 5206 and 5200 is associative
LCM of 5200 and 5206 = LCM of 5206 and 5200
1. What is the LCM of 5200 and 5206?
Answer: LCM of 5200 and 5206 is 13535600.
2. What are the Factors of 5200?
Answer: Factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200. There are 30 integers that are factors of 5200. The greatest factor of 5200 is 5200.
3. What are the Factors of 5206?
Answer: Factors of 5206 are 1, 2, 19, 38, 137, 274, 2603, 5206. There are 8 integers that are factors of 5206. The greatest factor of 5206 is 5206.
4. How to Find the LCM of 5200 and 5206?
Answer:
Least Common Multiple of 5200 and 5206 = 13535600
Step 1: Find the prime factorization of 5200
5200 = 2 x 2 x 2 x 2 x 5 x 5 x 13
Step 2: Find the prime factorization of 5206
5206 = 2 x 19 x 137
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 13535600 = 2 x 2 x 2 x 2 x 5 x 5 x 13 x 19 x 137
Step 4: Therefore, the least common multiple of 5200 and 5206 is 13535600.