Least Common Multiple (LCM) of 54 and 174
The least common multiple (LCM) of 54 and 174 is 1566.
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 54 and 174?
First, calculate the GCD of 54 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 174 = 0 remainder 54 |
| 2 | 174 ÷ 54 = 3 remainder 12 |
| 3 | 54 ÷ 12 = 4 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 29 | 1740 |
| 105 and 61 | 6405 |
| 136 and 26 | 1768 |
| 120 and 122 | 7320 |
| 157 and 183 | 28731 |