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 |
|---|---|
| 151 and 147 | 22197 |
| 131 and 100 | 13100 |
| 93 and 130 | 12090 |
| 179 and 45 | 8055 |
| 117 and 68 | 7956 |