Least Common Multiple (LCM) of 93 and 114
The least common multiple (LCM) of 93 and 114 is 3534.
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 93 and 114?
First, calculate the GCD of 93 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 114 = 0 remainder 93 |
| 2 | 114 ÷ 93 = 1 remainder 21 |
| 3 | 93 ÷ 21 = 4 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 23 | 2829 |
| 56 and 186 | 5208 |
| 136 and 69 | 9384 |
| 72 and 11 | 792 |
| 105 and 137 | 14385 |