Least Common Multiple (LCM) of 114 and 172
The least common multiple (LCM) of 114 and 172 is 9804.
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 114 and 172?
First, calculate the GCD of 114 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 172 = 0 remainder 114 |
| 2 | 172 ÷ 114 = 1 remainder 58 |
| 3 | 114 ÷ 58 = 1 remainder 56 |
| 4 | 58 ÷ 56 = 1 remainder 2 |
| 5 | 56 ÷ 2 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 32 | 5216 |
| 163 and 191 | 31133 |
| 48 and 102 | 816 |
| 121 and 36 | 4356 |
| 15 and 69 | 345 |