Least Common Multiple (LCM) of 54 and 14
The least common multiple (LCM) of 54 and 14 is 378.
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 14?
First, calculate the GCD of 54 and 14 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 14 = 3 remainder 12 |
| 2 | 14 ÷ 12 = 1 remainder 2 |
| 3 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 176 | 34320 |
| 120 and 105 | 840 |
| 46 and 177 | 8142 |
| 60 and 197 | 11820 |
| 169 and 67 | 11323 |