Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 199 and 200 the smallest integer that is 39800 that is divisible by both numbers.
Least Common Multiple (LCM) of 199 and 200 is 39800.
LCM(199,200) = 39800
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 199 and 200. First we will calculate the prime factors of 199 and 200.
Prime Factorization of 199
199 | 199 |
1 |
Prime factors of 199 are 199. Prime factorization of 199 in exponential form is:
199 = 1991
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 199 and 200.
LCM(199,200) = 23×52×1991
LCM(199,200) = 39800
Factors of 199
List of positive integer factors of 199 that divides 199 without a remainder.
1, 199
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 199 and 200, than apply into the LCM equation.
GCF(199,200) = 1
LCM(199,200) = ( 199 × 200) / 1
LCM(199,200) = 39800 / 1
LCM(199,200) = 39800
(i) The LCM of 200 and 199 is associative
LCM of 199 and 200 = LCM of 200 and 199
1. What is the LCM of 199 and 200?
Answer: LCM of 199 and 200 is 39800.
2. 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.
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 199 and 200?
Answer:
Least Common Multiple of 199 and 200 = 39800
Step 1: Find the prime factorization of 199
199 = 199
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 = 39800 = 2 x 2 x 2 x 5 x 5 x 199
Step 4: Therefore, the least common multiple of 199 and 200 is 39800.