Least Common Multiple (LCM) of 63 and 169
The least common multiple (LCM) of 63 and 169 is 10647.
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 63 and 169?
First, calculate the GCD of 63 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 169 = 0 remainder 63 |
| 2 | 169 ÷ 63 = 2 remainder 43 |
| 3 | 63 ÷ 43 = 1 remainder 20 |
| 4 | 43 ÷ 20 = 2 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 63 | 5229 |
| 28 and 79 | 2212 |
| 55 and 80 | 880 |
| 119 and 198 | 23562 |
| 34 and 71 | 2414 |