Least Common Multiple (LCM) of 20 and 151
The least common multiple (LCM) of 20 and 151 is 3020.
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 20 and 151?
First, calculate the GCD of 20 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 151 = 0 remainder 20 |
| 2 | 151 ÷ 20 = 7 remainder 11 |
| 3 | 20 ÷ 11 = 1 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 108 | 2484 |
| 184 and 112 | 2576 |
| 189 and 54 | 378 |
| 16 and 192 | 192 |
| 110 and 112 | 6160 |