Least Common Multiple (LCM) of 101 and 160
The least common multiple (LCM) of 101 and 160 is 16160.
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 160?
First, calculate the GCD of 101 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 160 = 0 remainder 101 |
| 2 | 160 ÷ 101 = 1 remainder 59 |
| 3 | 101 ÷ 59 = 1 remainder 42 |
| 4 | 59 ÷ 42 = 1 remainder 17 |
| 5 | 42 ÷ 17 = 2 remainder 8 |
| 6 | 17 ÷ 8 = 2 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 102 | 7854 |
| 29 and 149 | 4321 |
| 91 and 66 | 6006 |
| 141 and 142 | 20022 |
| 169 and 64 | 10816 |