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 |
|---|---|
| 167 and 127 | 21209 |
| 190 and 94 | 8930 |
| 107 and 193 | 20651 |
| 137 and 129 | 17673 |
| 94 and 146 | 6862 |