Least Common Multiple (LCM) of 120 and 174
The least common multiple (LCM) of 120 and 174 is 3480.
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 120 and 174?
First, calculate the GCD of 120 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 174 = 0 remainder 120 |
| 2 | 174 ÷ 120 = 1 remainder 54 |
| 3 | 120 ÷ 54 = 2 remainder 12 |
| 4 | 54 ÷ 12 = 4 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 102 | 2550 |
| 20 and 100 | 100 |
| 138 and 169 | 23322 |
| 22 and 29 | 638 |
| 39 and 156 | 156 |