Least Common Multiple (LCM) of 72 and 118
The least common multiple (LCM) of 72 and 118 is 4248.
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 118?
First, calculate the GCD of 72 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 118 = 0 remainder 72 |
| 2 | 118 ÷ 72 = 1 remainder 46 |
| 3 | 72 ÷ 46 = 1 remainder 26 |
| 4 | 46 ÷ 26 = 1 remainder 20 |
| 5 | 26 ÷ 20 = 1 remainder 6 |
| 6 | 20 ÷ 6 = 3 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 186 | 930 |
| 16 and 46 | 368 |
| 178 and 166 | 14774 |
| 20 and 145 | 580 |
| 69 and 69 | 69 |