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 |
|---|---|
| 140 and 123 | 17220 |
| 98 and 186 | 9114 |
| 57 and 109 | 6213 |
| 106 and 57 | 6042 |
| 89 and 122 | 10858 |