Least Common Multiple (LCM) of 48 and 21
The least common multiple (LCM) of 48 and 21 is 336.
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 21?
First, calculate the GCD of 48 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 21 = 2 remainder 6 |
| 2 | 21 ÷ 6 = 3 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 38 | 3496 |
| 71 and 122 | 8662 |
| 165 and 67 | 11055 |
| 29 and 94 | 2726 |
| 158 and 24 | 1896 |