Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5198 and 5206 the smallest integer that is 13530394 that is divisible by both numbers.
Least Common Multiple (LCM) of 5198 and 5206 is 13530394.
LCM(5198,5206) = 13530394
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 5198 and 5206. First we will calculate the prime factors of 5198 and 5206.
Prime Factorization of 5198
2 | 5198 |
23 | 2599 |
113 | 113 |
1 |
Prime factors of 5198 are 2, 23,113. Prime factorization of 5198 in exponential form is:
5198 = 21×231×1131
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 5198 and 5206.
LCM(5198,5206) = 21×191×231×1131×1371
LCM(5198,5206) = 13530394
Factors of 5198
List of positive integer factors of 5198 that divides 5198 without a remainder.
1, 2, 23, 46, 113, 226, 2599, 5198
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 5198 and 5206, than apply into the LCM equation.
GCF(5198,5206) = 2
LCM(5198,5206) = ( 5198 × 5206) / 2
LCM(5198,5206) = 27060788 / 2
LCM(5198,5206) = 13530394
(i) The LCM of 5206 and 5198 is associative
LCM of 5198 and 5206 = LCM of 5206 and 5198
1. What is the LCM of 5198 and 5206?
Answer: LCM of 5198 and 5206 is 13530394.
2. What are the Factors of 5198?
Answer: Factors of 5198 are 1, 2, 23, 46, 113, 226, 2599, 5198. There are 8 integers that are factors of 5198. The greatest factor of 5198 is 5198.
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 5198 and 5206?
Answer:
Least Common Multiple of 5198 and 5206 = 13530394
Step 1: Find the prime factorization of 5198
5198 = 2 x 23 x 113
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 = 13530394 = 2 x 19 x 23 x 113 x 137
Step 4: Therefore, the least common multiple of 5198 and 5206 is 13530394.