Least Common Multiple (LCM) of 93 and 117
The least common multiple (LCM) of 93 and 117 is 3627.
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 117?
First, calculate the GCD of 93 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 117 = 0 remainder 93 |
| 2 | 117 ÷ 93 = 1 remainder 24 |
| 3 | 93 ÷ 24 = 3 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 106 | 14310 |
| 49 and 60 | 2940 |
| 113 and 184 | 20792 |
| 109 and 29 | 3161 |
| 170 and 106 | 9010 |