Least Common Multiple of 105 and 112
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 112 the smallest integer that is 1680 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 112 is 1680.
LCM(105,112) = 1680
LCM of 105 and 112
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 112 by Prime method
- Least Common Multiple of 105 and 112 with GCF Formula
LCM of 105 and 112 is 1680
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 112. First we will calculate the prime factors of 105 and 112.
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 112
| 2 | 112 |
| 2 | 56 |
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:
112 = 24×71
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 112.
LCM(105,112) = 24×31×51×71
LCM(105,112) = 1680
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 112
List of positive integer factors of 112 that divides 112 without a remainder.
1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Least Common Multiple of 105 and 112 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 112, than apply into the LCM equation.
GCF(105,112) = 7
LCM(105,112) = ( 105 × 112) / 7
LCM(105,112) = 11760 / 7
LCM(105,112) = 1680
Properties of LCM 105 and 112
(i) The LCM of 112 and 105 is associative
LCM of 105 and 112 = LCM of 112 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 112
Frequently Asked Questions on LCM of 105 and 112
1. What is the LCM of 105 and 112?
Answer: LCM of 105 and 112 is 1680.
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 112?
Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.
4. How to Find the LCM of 105 and 112?
Answer:
Least Common Multiple of 105 and 112 = 1680
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 112
112 = 2 x 2 x 2 x 2 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 = 1680 = 2 x 2 x 2 x 2 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 105 and 112 is 1680.
