Least Common Multiple (LCM) of 54 and 98
The least common multiple (LCM) of 54 and 98 is 2646.
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 98?
First, calculate the GCD of 54 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 98 = 0 remainder 54 |
| 2 | 98 ÷ 54 = 1 remainder 44 |
| 3 | 54 ÷ 44 = 1 remainder 10 |
| 4 | 44 ÷ 10 = 4 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 83 | 11454 |
| 148 and 169 | 25012 |
| 90 and 37 | 3330 |
| 106 and 32 | 1696 |
| 138 and 196 | 13524 |