Least Common Multiple (LCM) of 75 and 162
The least common multiple (LCM) of 75 and 162 is 4050.
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 75 and 162?
First, calculate the GCD of 75 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 162 = 0 remainder 75 |
| 2 | 162 ÷ 75 = 2 remainder 12 |
| 3 | 75 ÷ 12 = 6 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 169 | 10309 |
| 112 and 129 | 14448 |
| 39 and 51 | 663 |
| 62 and 196 | 6076 |
| 88 and 110 | 440 |