Least Common Multiple (LCM) of 72 and 112
The least common multiple (LCM) of 72 and 112 is 1008.
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 72 and 112?
First, calculate the GCD of 72 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 112 = 0 remainder 72 |
| 2 | 112 ÷ 72 = 1 remainder 40 |
| 3 | 72 ÷ 40 = 1 remainder 32 |
| 4 | 40 ÷ 32 = 1 remainder 8 |
| 5 | 32 ÷ 8 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 121 | 8712 |
| 42 and 25 | 1050 |
| 195 and 42 | 2730 |
| 162 and 43 | 6966 |
| 42 and 84 | 84 |