Least Common Multiple (LCM) of 118 and 172
The least common multiple (LCM) of 118 and 172 is 10148.
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 172?
First, calculate the GCD of 118 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 172 = 0 remainder 118 |
| 2 | 172 ÷ 118 = 1 remainder 54 |
| 3 | 118 ÷ 54 = 2 remainder 10 |
| 4 | 54 ÷ 10 = 5 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 24 | 216 |
| 117 and 118 | 13806 |
| 122 and 14 | 854 |
| 75 and 118 | 8850 |
| 32 and 152 | 608 |