Least Common Multiple of 103 and 105
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 103 and 105 the smallest integer that is 10815 that is divisible by both numbers.
Least Common Multiple (LCM) of 103 and 105 is 10815.
LCM(103,105) = 10815
LCM of 103 and 105
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 103 and 105 by Prime method
- Least Common Multiple of 103 and 105 with GCF Formula
LCM of 103 and 105 is 10815
Least common multiple can be found by multiplying the highest exponent prime factors of 103 and 105. First we will calculate the prime factors of 103 and 105.
Prime Factorization of 103
| 103 | 103 |
| 1 |
Prime factors of 103 are 103. Prime factorization of 103 in exponential form is:
103 = 1031
Prime Factorization of 105
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 105 are 3, 5,7. Prime factorization of 105 in exponential form is:
105 = 31×51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 103 and 105.
LCM(103,105) = 31×51×71×1031
LCM(103,105) = 10815
Factors of 103
List of positive integer factors of 103 that divides 103 without a remainder.
1, 103
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1, 3, 5, 7, 15, 21, 35, 105
Least Common Multiple of 103 and 105 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 103 and 105, than apply into the LCM equation.
GCF(103,105) = 1
LCM(103,105) = ( 103 × 105) / 1
LCM(103,105) = 10815 / 1
LCM(103,105) = 10815
Properties of LCM 103 and 105
(i) The LCM of 105 and 103 is associative
LCM of 103 and 105 = LCM of 105 and 103
Related Least Common Multiples of 103
Related Least Common Multiples of 105
Frequently Asked Questions on LCM of 103 and 105
1. What is the LCM of 103 and 105?
Answer: LCM of 103 and 105 is 10815.
2. 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.
3. What are the Factors of 105?
Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.
4. How to Find the LCM of 103 and 105?
Answer:
Least Common Multiple of 103 and 105 = 10815
Step 1: Find the prime factorization of 103
103 = 103
Step 2: Find the prime factorization of 105
105 = 3 x 5 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 = 10815 = 3 x 5 x 7 x 103
Step 4: Therefore, the least common multiple of 103 and 105 is 10815.