Least Common Multiple (LCM) of 93 and 145
The least common multiple (LCM) of 93 and 145 is 13485.
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 145?
First, calculate the GCD of 93 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 145 = 0 remainder 93 |
| 2 | 145 ÷ 93 = 1 remainder 52 |
| 3 | 93 ÷ 52 = 1 remainder 41 |
| 4 | 52 ÷ 41 = 1 remainder 11 |
| 5 | 41 ÷ 11 = 3 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 108 | 1404 |
| 46 and 138 | 138 |
| 173 and 148 | 25604 |
| 82 and 170 | 6970 |
| 183 and 173 | 31659 |