Least Common Multiple of 102 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 102 and 105 the smallest integer that is 3570 that is divisible by both numbers.
Least Common Multiple (LCM) of 102 and 105 is 3570.
LCM(102,105) = 3570
LCM of 102 and 105
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 102 and 105 by Prime method
- Least Common Multiple of 102 and 105 with GCF Formula
LCM of 102 and 105 is 3570
Least common multiple can be found by multiplying the highest exponent prime factors of 102 and 105. First we will calculate the prime factors of 102 and 105.
Prime Factorization of 102
| 2 | 102 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 102 are 2, 3,17. Prime factorization of 102 in exponential form is:
102 = 21×31×171
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 102 and 105.
LCM(102,105) = 21×31×51×71×171
LCM(102,105) = 3570
Factors of 102
List of positive integer factors of 102 that divides 102 without a remainder.
1, 2, 3, 6, 17, 34, 51, 102
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 102 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 102 and 105, than apply into the LCM equation.
GCF(102,105) = 3
LCM(102,105) = ( 102 × 105) / 3
LCM(102,105) = 10710 / 3
LCM(102,105) = 3570
Properties of LCM 102 and 105
(i) The LCM of 105 and 102 is associative
LCM of 102 and 105 = LCM of 105 and 102
Related Least Common Multiples of 102
Related Least Common Multiples of 105
Frequently Asked Questions on LCM of 102 and 105
1. What is the LCM of 102 and 105?
Answer: LCM of 102 and 105 is 3570.
2. What are the Factors of 102?
Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.
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 102 and 105?
Answer:
Least Common Multiple of 102 and 105 = 3570
Step 1: Find the prime factorization of 102
102 = 2 x 3 x 17
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 = 3570 = 2 x 3 x 5 x 7 x 17
Step 4: Therefore, the least common multiple of 102 and 105 is 3570.
