Least Common Multiple (LCM) of 100 and 151
The least common multiple (LCM) of 100 and 151 is 15100.
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 100 and 151?
First, calculate the GCD of 100 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 151 = 0 remainder 100 |
| 2 | 151 ÷ 100 = 1 remainder 51 |
| 3 | 100 ÷ 51 = 1 remainder 49 |
| 4 | 51 ÷ 49 = 1 remainder 2 |
| 5 | 49 ÷ 2 = 24 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 52 | 2756 |
| 140 and 126 | 1260 |
| 189 and 101 | 19089 |
| 82 and 133 | 10906 |
| 13 and 56 | 728 |