Least Common Multiple (LCM) of 169 and 100
The least common multiple (LCM) of 169 and 100 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 169 and 100?
First, calculate the GCD of 169 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 100 = 1 remainder 69 |
| 2 | 100 ÷ 69 = 1 remainder 31 |
| 3 | 69 ÷ 31 = 2 remainder 7 |
| 4 | 31 ÷ 7 = 4 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 199 | 35820 |
| 37 and 165 | 6105 |
| 136 and 63 | 8568 |
| 184 and 35 | 6440 |
| 31 and 137 | 4247 |