Least Common Multiple (LCM) of 74 and 54
The least common multiple (LCM) of 74 and 54 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 74 and 54?
First, calculate the GCD of 74 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 54 = 1 remainder 20 |
| 2 | 54 ÷ 20 = 2 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 10 | 830 |
| 114 and 31 | 3534 |
| 146 and 112 | 8176 |
| 14 and 106 | 742 |
| 187 and 180 | 33660 |