Least Common Multiple (LCM) of 113 and 70
The least common multiple (LCM) of 113 and 70 is 7910.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 70?
First, calculate the GCD of 113 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 70 = 1 remainder 43 |
| 2 | 70 ÷ 43 = 1 remainder 27 |
| 3 | 43 ÷ 27 = 1 remainder 16 |
| 4 | 27 ÷ 16 = 1 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 186 | 3906 |
| 88 and 163 | 14344 |
| 136 and 55 | 7480 |
| 24 and 105 | 840 |
| 101 and 114 | 11514 |