Least Common Multiple (LCM) of 93 and 107
The least common multiple (LCM) of 93 and 107 is 9951.
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 107?
First, calculate the GCD of 93 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 107 = 0 remainder 93 |
| 2 | 107 ÷ 93 = 1 remainder 14 |
| 3 | 93 ÷ 14 = 6 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 81 | 9153 |
| 110 and 69 | 7590 |
| 93 and 36 | 1116 |
| 112 and 168 | 336 |
| 150 and 112 | 8400 |