Least Common Multiple (LCM) of 54 and 74
The least common multiple (LCM) of 54 and 74 is 1998.
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 74?
First, calculate the GCD of 54 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 74 = 0 remainder 54 |
| 2 | 74 ÷ 54 = 1 remainder 20 |
| 3 | 54 ÷ 20 = 2 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 52 | 364 |
| 41 and 190 | 7790 |
| 138 and 180 | 4140 |
| 109 and 65 | 7085 |
| 153 and 87 | 4437 |