Least Common Multiple (LCM) of 116 and 172
The least common multiple (LCM) of 116 and 172 is 4988.
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 116 and 172?
First, calculate the GCD of 116 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 172 = 0 remainder 116 |
| 2 | 172 ÷ 116 = 1 remainder 56 |
| 3 | 116 ÷ 56 = 2 remainder 4 |
| 4 | 56 ÷ 4 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 109 | 15478 |
| 157 and 69 | 10833 |
| 62 and 142 | 4402 |
| 117 and 170 | 19890 |
| 35 and 154 | 770 |