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 |
|---|---|
| 159 and 139 | 22101 |
| 172 and 78 | 6708 |
| 141 and 30 | 1410 |
| 76 and 149 | 11324 |
| 36 and 200 | 1800 |