Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 196 and 200 the smallest integer that is 9800 that is divisible by both numbers.
Least Common Multiple (LCM) of 196 and 200 is 9800.
LCM(196,200) = 9800
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 196 and 200. First we will calculate the prime factors of 196 and 200.
Prime Factorization of 196
2 | 196 |
2 | 98 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 196 are 2,7. Prime factorization of 196 in exponential form is:
196 = 22×72
Prime Factorization of 200
2 | 200 |
2 | 100 |
2 | 50 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 200 are 2,5. Prime factorization of 200 in exponential form is:
200 = 23×52
Now multiplying the highest exponent prime factors to calculate the LCM of 196 and 200.
LCM(196,200) = 23×52×72
LCM(196,200) = 9800
Factors of 196
List of positive integer factors of 196 that divides 196 without a remainder.
1, 2, 4, 7, 14, 28, 49, 98, 196
Factors of 200
List of positive integer factors of 200 that divides 200 without a remainder.
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 196 and 200, than apply into the LCM equation.
GCF(196,200) = 4
LCM(196,200) = ( 196 × 200) / 4
LCM(196,200) = 39200 / 4
LCM(196,200) = 9800
(i) The LCM of 200 and 196 is associative
LCM of 196 and 200 = LCM of 200 and 196
1. What is the LCM of 196 and 200?
Answer: LCM of 196 and 200 is 9800.
2. What are the Factors of 196?
Answer: Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. There are 9 integers that are factors of 196. The greatest factor of 196 is 196.
3. What are the Factors of 200?
Answer: Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. There are 12 integers that are factors of 200. The greatest factor of 200 is 200.
4. How to Find the LCM of 196 and 200?
Answer:
Least Common Multiple of 196 and 200 = 9800
Step 1: Find the prime factorization of 196
196 = 2 x 2 x 7 x 7
Step 2: Find the prime factorization of 200
200 = 2 x 2 x 2 x 5 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9800 = 2 x 2 x 2 x 5 x 5 x 7 x 7
Step 4: Therefore, the least common multiple of 196 and 200 is 9800.