Least Common Multiple (LCM) of 17 and 151
The least common multiple (LCM) of 17 and 151 is 2567.
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 17 and 151?
First, calculate the GCD of 17 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 151 = 0 remainder 17 |
| 2 | 151 ÷ 17 = 8 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 75 | 7950 |
| 75 and 142 | 10650 |
| 102 and 52 | 2652 |
| 19 and 117 | 2223 |
| 135 and 153 | 2295 |