Least Common Multiple (LCM) of 64 and 169
The least common multiple (LCM) of 64 and 169 is 10816.
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 64 and 169?
First, calculate the GCD of 64 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 169 = 0 remainder 64 |
| 2 | 169 ÷ 64 = 2 remainder 41 |
| 3 | 64 ÷ 41 = 1 remainder 23 |
| 4 | 41 ÷ 23 = 1 remainder 18 |
| 5 | 23 ÷ 18 = 1 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 |
|---|---|
| 50 and 105 | 1050 |
| 182 and 171 | 31122 |
| 173 and 67 | 11591 |
| 133 and 109 | 14497 |
| 122 and 154 | 9394 |