Least Common Multiple (LCM) of 48 and 70
The least common multiple (LCM) of 48 and 70 is 1680.
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 70?
First, calculate the GCD of 48 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 70 = 0 remainder 48 |
| 2 | 70 ÷ 48 = 1 remainder 22 |
| 3 | 48 ÷ 22 = 2 remainder 4 |
| 4 | 22 ÷ 4 = 5 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 155 | 25265 |
| 54 and 189 | 378 |
| 101 and 22 | 2222 |
| 70 and 129 | 9030 |
| 47 and 38 | 1786 |