Least Common Multiple (LCM) of 118 and 72
The least common multiple (LCM) of 118 and 72 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 118 and 72?
First, calculate the GCD of 118 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 72 = 1 remainder 46 |
| 2 | 72 ÷ 46 = 1 remainder 26 |
| 3 | 46 ÷ 26 = 1 remainder 20 |
| 4 | 26 ÷ 20 = 1 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 103 | 18643 |
| 32 and 56 | 224 |
| 73 and 200 | 14600 |
| 129 and 198 | 8514 |
| 117 and 193 | 22581 |