Least Common Multiple (LCM) of 54 and 93
The least common multiple (LCM) of 54 and 93 is 1674.
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 93?
First, calculate the GCD of 54 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 93 = 0 remainder 54 |
| 2 | 93 ÷ 54 = 1 remainder 39 |
| 3 | 54 ÷ 39 = 1 remainder 15 |
| 4 | 39 ÷ 15 = 2 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 33 | 759 |
| 142 and 55 | 7810 |
| 110 and 97 | 10670 |
| 160 and 129 | 20640 |
| 138 and 103 | 14214 |