Least Common Multiple (LCM) of 180 and 48
The least common multiple (LCM) of 180 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 180 and 48?
First, calculate the GCD of 180 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 48 = 3 remainder 36 |
| 2 | 48 ÷ 36 = 1 remainder 12 |
| 3 | 36 ÷ 12 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 68 | 10676 |
| 174 and 152 | 13224 |
| 62 and 141 | 8742 |
| 78 and 78 | 78 |
| 126 and 103 | 12978 |