Least Common Multiple (LCM) of 100 and 169
The least common multiple (LCM) of 100 and 169 is 16900.
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 169?
First, calculate the GCD of 100 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 169 = 0 remainder 100 |
| 2 | 169 ÷ 100 = 1 remainder 69 |
| 3 | 100 ÷ 69 = 1 remainder 31 |
| 4 | 69 ÷ 31 = 2 remainder 7 |
| 5 | 31 ÷ 7 = 4 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 190 | 1520 |
| 96 and 158 | 7584 |
| 58 and 120 | 3480 |
| 85 and 63 | 5355 |
| 75 and 63 | 1575 |