Least Common Multiple (LCM) of 153 and 180
The least common multiple (LCM) of 153 and 180 is 3060.
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 153 and 180?
First, calculate the GCD of 153 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 180 = 0 remainder 153 |
| 2 | 180 ÷ 153 = 1 remainder 27 |
| 3 | 153 ÷ 27 = 5 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 62 | 1116 |
| 21 and 111 | 777 |
| 71 and 39 | 2769 |
| 196 and 75 | 14700 |
| 104 and 116 | 3016 |