Least Common Multiple (LCM) of 162 and 35
The least common multiple (LCM) of 162 and 35 is 5670.
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 162 and 35?
First, calculate the GCD of 162 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 35 = 4 remainder 22 |
| 2 | 35 ÷ 22 = 1 remainder 13 |
| 3 | 22 ÷ 13 = 1 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 176 | 22704 |
| 61 and 90 | 5490 |
| 135 and 195 | 1755 |
| 185 and 126 | 23310 |
| 82 and 67 | 5494 |