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 199 the smallest integer that is 39004 that is divisible by both numbers.
Least Common Multiple (LCM) of 196 and 199 is 39004.
LCM(196,199) = 39004
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 199. First we will calculate the prime factors of 196 and 199.
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 199
199 | 199 |
1 |
Prime factors of 199 are 199. Prime factorization of 199 in exponential form is:
199 = 1991
Now multiplying the highest exponent prime factors to calculate the LCM of 196 and 199.
LCM(196,199) = 22×72×1991
LCM(196,199) = 39004
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 199
List of positive integer factors of 199 that divides 199 without a remainder.
1, 199
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 196 and 199, than apply into the LCM equation.
GCF(196,199) = 1
LCM(196,199) = ( 196 × 199) / 1
LCM(196,199) = 39004 / 1
LCM(196,199) = 39004
(i) The LCM of 199 and 196 is associative
LCM of 196 and 199 = LCM of 199 and 196
1. What is the LCM of 196 and 199?
Answer: LCM of 196 and 199 is 39004.
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 199?
Answer: Factors of 199 are 1, 199. There are 2 integers that are factors of 199. The greatest factor of 199 is 199.
4. How to Find the LCM of 196 and 199?
Answer:
Least Common Multiple of 196 and 199 = 39004
Step 1: Find the prime factorization of 196
196 = 2 x 2 x 7 x 7
Step 2: Find the prime factorization of 199
199 = 199
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 39004 = 2 x 2 x 7 x 7 x 199
Step 4: Therefore, the least common multiple of 196 and 199 is 39004.