Least Common Multiple of 105 and 539
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 105 and 539 the smallest integer that is 8085 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 539 is 8085.
LCM(105,539) = 8085
LCM of 105 and 539
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 539 by Prime method
- Least Common Multiple of 105 and 539 with GCF Formula
LCM of 105 and 539 is 8085
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 539. First we will calculate the prime factors of 105 and 539.
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
Prime Factorization of 539
| 7 | 539 |
| 7 | 77 |
| 11 | 11 |
| 1 |
Prime factors of 539 are 7,11. Prime factorization of 539 in exponential form is:
539 = 72×111
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 539.
LCM(105,539) = 31×51×72×111
LCM(105,539) = 8085
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1, 3, 5, 7, 15, 21, 35, 105
Factors of 539
List of positive integer factors of 539 that divides 539 without a remainder.
1, 7, 11, 49, 77, 539
Least Common Multiple of 105 and 539 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 539, than apply into the LCM equation.
GCF(105,539) = 7
LCM(105,539) = ( 105 × 539) / 7
LCM(105,539) = 56595 / 7
LCM(105,539) = 8085
Properties of LCM 105 and 539
(i) The LCM of 539 and 105 is associative
LCM of 105 and 539 = LCM of 539 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 539
Frequently Asked Questions on LCM of 105 and 539
1. What is the LCM of 105 and 539?
Answer: LCM of 105 and 539 is 8085.
2. 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.
3. What are the Factors of 539?
Answer: Factors of 539 are 1, 7, 11, 49, 77, 539. There are 6 integers that are factors of 539. The greatest factor of 539 is 539.
4. How to Find the LCM of 105 and 539?
Answer:
Least Common Multiple of 105 and 539 = 8085
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 539
539 = 7 x 7 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8085 = 3 x 5 x 7 x 7 x 11
Step 4: Therefore, the least common multiple of 105 and 539 is 8085.