Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 99 and 103 the smallest integer that is 10197 that is divisible by both numbers.
Least Common Multiple (LCM) of 99 and 103 is 10197.
LCM(99,103) = 10197
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 99 and 103. First we will calculate the prime factors of 99 and 103.
Prime Factorization of 99
3 | 99 |
3 | 33 |
11 | 11 |
1 |
Prime factors of 99 are 3,11. Prime factorization of 99 in exponential form is:
99 = 32×111
Prime Factorization of 103
103 | 103 |
1 |
Prime factors of 103 are 103. Prime factorization of 103 in exponential form is:
103 = 1031
Now multiplying the highest exponent prime factors to calculate the LCM of 99 and 103.
LCM(99,103) = 32×111×1031
LCM(99,103) = 10197
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1, 3, 9, 11, 33, 99
Factors of 103
List of positive integer factors of 103 that divides 103 without a remainder.
1, 103
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 99 and 103, than apply into the LCM equation.
GCF(99,103) = 1
LCM(99,103) = ( 99 × 103) / 1
LCM(99,103) = 10197 / 1
LCM(99,103) = 10197
(i) The LCM of 103 and 99 is associative
LCM of 99 and 103 = LCM of 103 and 99
1. What is the LCM of 99 and 103?
Answer: LCM of 99 and 103 is 10197.
2. What are the Factors of 99?
Answer: Factors of 99 are 1, 3, 9, 11, 33, 99. There are 6 integers that are factors of 99. The greatest factor of 99 is 99.
3. What are the Factors of 103?
Answer: Factors of 103 are 1, 103. There are 2 integers that are factors of 103. The greatest factor of 103 is 103.
4. How to Find the LCM of 99 and 103?
Answer:
Least Common Multiple of 99 and 103 = 10197
Step 1: Find the prime factorization of 99
99 = 3 x 3 x 11
Step 2: Find the prime factorization of 103
103 = 103
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 10197 = 3 x 3 x 11 x 103
Step 4: Therefore, the least common multiple of 99 and 103 is 10197.