Least Common Multiple (LCM) of 100 and 159
The least common multiple (LCM) of 100 and 159 is 15900.
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 159?
First, calculate the GCD of 100 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 159 = 0 remainder 100 |
| 2 | 159 ÷ 100 = 1 remainder 59 |
| 3 | 100 ÷ 59 = 1 remainder 41 |
| 4 | 59 ÷ 41 = 1 remainder 18 |
| 5 | 41 ÷ 18 = 2 remainder 5 |
| 6 | 18 ÷ 5 = 3 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 120 | 2760 |
| 113 and 36 | 4068 |
| 42 and 22 | 462 |
| 124 and 33 | 4092 |
| 157 and 153 | 24021 |