Least Common Multiple (LCM) of 112 and 70
The least common multiple (LCM) of 112 and 70 is 560.
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 112 and 70?
First, calculate the GCD of 112 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 70 = 1 remainder 42 |
| 2 | 70 ÷ 42 = 1 remainder 28 |
| 3 | 42 ÷ 28 = 1 remainder 14 |
| 4 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 54 | 378 |
| 60 and 190 | 1140 |
| 138 and 23 | 138 |
| 46 and 75 | 3450 |
| 85 and 110 | 1870 |