Least Common Multiple (LCM) of 171 and 120
The least common multiple (LCM) of 171 and 120 is 6840.
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 171 and 120?
First, calculate the GCD of 171 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 120 = 1 remainder 51 |
| 2 | 120 ÷ 51 = 2 remainder 18 |
| 3 | 51 ÷ 18 = 2 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 96 | 2784 |
| 199 and 144 | 28656 |
| 73 and 22 | 1606 |
| 10 and 136 | 680 |
| 114 and 164 | 9348 |