Least Common Multiple (LCM) of 90 and 48
The least common multiple (LCM) of 90 and 48 is 720.
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 90 and 48?
First, calculate the GCD of 90 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 48 = 1 remainder 42 |
| 2 | 48 ÷ 42 = 1 remainder 6 |
| 3 | 42 ÷ 6 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 49 | 588 |
| 101 and 129 | 13029 |
| 163 and 157 | 25591 |
| 80 and 148 | 2960 |
| 80 and 120 | 240 |