Least Common Multiple (LCM) of 112 and 60
The least common multiple (LCM) of 112 and 60 is 1680.
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 60?
First, calculate the GCD of 112 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 60 = 1 remainder 52 |
| 2 | 60 ÷ 52 = 1 remainder 8 |
| 3 | 52 ÷ 8 = 6 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 48 | 336 |
| 190 and 196 | 18620 |
| 174 and 101 | 17574 |
| 112 and 87 | 9744 |
| 175 and 193 | 33775 |