Least Common Multiple of 105 and 109
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 109 the smallest integer that is 11445 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 109 is 11445.
LCM(105,109) = 11445
LCM of 105 and 109
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 109 by Prime method
- Least Common Multiple of 105 and 109 with GCF Formula
LCM of 105 and 109 is 11445
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 109. First we will calculate the prime factors of 105 and 109.
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 109
| 109 | 109 |
| 1 |
Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:
109 = 1091
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 109.
LCM(105,109) = 31×51×71×1091
LCM(105,109) = 11445
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 109
List of positive integer factors of 109 that divides 109 without a remainder.
1, 109
Least Common Multiple of 105 and 109 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 109, than apply into the LCM equation.
GCF(105,109) = 1
LCM(105,109) = ( 105 × 109) / 1
LCM(105,109) = 11445 / 1
LCM(105,109) = 11445
Properties of LCM 105 and 109
(i) The LCM of 109 and 105 is associative
LCM of 105 and 109 = LCM of 109 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 109
Frequently Asked Questions on LCM of 105 and 109
1. What is the LCM of 105 and 109?
Answer: LCM of 105 and 109 is 11445.
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 109?
Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.
4. How to Find the LCM of 105 and 109?
Answer:
Least Common Multiple of 105 and 109 = 11445
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 109
109 = 109
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11445 = 3 x 5 x 7 x 109
Step 4: Therefore, the least common multiple of 105 and 109 is 11445.