Least Common Multiple (LCM) of 48 and 106
The least common multiple (LCM) of 48 and 106 is 2544.
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 48 and 106?
First, calculate the GCD of 48 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 106 = 0 remainder 48 |
| 2 | 106 ÷ 48 = 2 remainder 10 |
| 3 | 48 ÷ 10 = 4 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 177 | 17700 |
| 67 and 87 | 5829 |
| 173 and 177 | 30621 |
| 140 and 42 | 420 |
| 112 and 26 | 1456 |