Least Common Multiple (LCM) of 152 and 180
The least common multiple (LCM) of 152 and 180 is 6840.
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 152 and 180?
First, calculate the GCD of 152 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 180 = 0 remainder 152 |
| 2 | 180 ÷ 152 = 1 remainder 28 |
| 3 | 152 ÷ 28 = 5 remainder 12 |
| 4 | 28 ÷ 12 = 2 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 73 | 5621 |
| 69 and 89 | 6141 |
| 184 and 112 | 2576 |
| 105 and 39 | 1365 |
| 142 and 174 | 12354 |