Least Common Multiple (LCM) of 106 and 54
The least common multiple (LCM) of 106 and 54 is 2862.
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 106 and 54?
First, calculate the GCD of 106 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 54 = 1 remainder 52 |
| 2 | 54 ÷ 52 = 1 remainder 2 |
| 3 | 52 ÷ 2 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 190 | 11970 |
| 171 and 140 | 23940 |
| 161 and 106 | 17066 |
| 161 and 187 | 30107 |
| 115 and 140 | 3220 |