Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2198 and 2205 the smallest integer that is 692370 that is divisible by both numbers.
Least Common Multiple (LCM) of 2198 and 2205 is 692370.
LCM(2198,2205) = 692370
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 2198 and 2205. First we will calculate the prime factors of 2198 and 2205.
Prime Factorization of 2198
2 | 2198 |
7 | 1099 |
157 | 157 |
1 |
Prime factors of 2198 are 2, 7,157. Prime factorization of 2198 in exponential form is:
2198 = 21×71×1571
Prime Factorization of 2205
3 | 2205 |
3 | 735 |
5 | 245 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 2205 are 3, 5,7. Prime factorization of 2205 in exponential form is:
2205 = 32×51×72
Now multiplying the highest exponent prime factors to calculate the LCM of 2198 and 2205.
LCM(2198,2205) = 21×32×51×72×1571
LCM(2198,2205) = 692370
Factors of 2198
List of positive integer factors of 2198 that divides 2198 without a remainder.
1, 2, 7, 14, 157, 314, 1099, 2198
Factors of 2205
List of positive integer factors of 2205 that divides 2205 without a remainder.
1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2198 and 2205, than apply into the LCM equation.
GCF(2198,2205) = 7
LCM(2198,2205) = ( 2198 × 2205) / 7
LCM(2198,2205) = 4846590 / 7
LCM(2198,2205) = 692370
(i) The LCM of 2205 and 2198 is associative
LCM of 2198 and 2205 = LCM of 2205 and 2198
1. What is the LCM of 2198 and 2205?
Answer: LCM of 2198 and 2205 is 692370.
2. What are the Factors of 2198?
Answer: Factors of 2198 are 1, 2, 7, 14, 157, 314, 1099, 2198. There are 8 integers that are factors of 2198. The greatest factor of 2198 is 2198.
3. What are the Factors of 2205?
Answer: Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205. There are 18 integers that are factors of 2205. The greatest factor of 2205 is 2205.
4. How to Find the LCM of 2198 and 2205?
Answer:
Least Common Multiple of 2198 and 2205 = 692370
Step 1: Find the prime factorization of 2198
2198 = 2 x 7 x 157
Step 2: Find the prime factorization of 2205
2205 = 3 x 3 x 5 x 7 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 692370 = 2 x 3 x 3 x 5 x 7 x 7 x 157
Step 4: Therefore, the least common multiple of 2198 and 2205 is 692370.