Least Common Multiple (LCM) of 35 and 162
The least common multiple (LCM) of 35 and 162 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 35 and 162?
First, calculate the GCD of 35 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 162 = 0 remainder 35 |
| 2 | 162 ÷ 35 = 4 remainder 22 |
| 3 | 35 ÷ 22 = 1 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 45 | 4095 |
| 28 and 80 | 560 |
| 127 and 100 | 12700 |
| 130 and 148 | 9620 |
| 128 and 163 | 20864 |