Least Common Multiple (LCM) of 101 and 162
The least common multiple (LCM) of 101 and 162 is 16362.
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 101 and 162?
First, calculate the GCD of 101 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 162 = 0 remainder 101 |
| 2 | 162 ÷ 101 = 1 remainder 61 |
| 3 | 101 ÷ 61 = 1 remainder 40 |
| 4 | 61 ÷ 40 = 1 remainder 21 |
| 5 | 40 ÷ 21 = 1 remainder 19 |
| 6 | 21 ÷ 19 = 1 remainder 2 |
| 7 | 19 ÷ 2 = 9 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 136 | 24888 |
| 178 and 174 | 15486 |
| 10 and 41 | 410 |
| 182 and 82 | 7462 |
| 171 and 191 | 32661 |