Least Common Multiple (LCM) of 48 and 101
The least common multiple (LCM) of 48 and 101 is 4848.
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 101?
First, calculate the GCD of 48 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 101 = 0 remainder 48 |
| 2 | 101 ÷ 48 = 2 remainder 5 |
| 3 | 48 ÷ 5 = 9 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 37 | 3293 |
| 52 and 135 | 7020 |
| 144 and 151 | 21744 |
| 126 and 26 | 1638 |
| 175 and 194 | 33950 |