Least Common Multiple (LCM) of 54 and 148
The least common multiple (LCM) of 54 and 148 is 3996.
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 148?
First, calculate the GCD of 54 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 148 = 0 remainder 54 |
| 2 | 148 ÷ 54 = 2 remainder 40 |
| 3 | 54 ÷ 40 = 1 remainder 14 |
| 4 | 40 ÷ 14 = 2 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 149 | 12516 |
| 137 and 34 | 4658 |
| 89 and 87 | 7743 |
| 32 and 197 | 6304 |
| 189 and 71 | 13419 |