Least Common Multiple (LCM) of 53 and 169
The least common multiple (LCM) of 53 and 169 is 8957.
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 53 and 169?
First, calculate the GCD of 53 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 169 = 0 remainder 53 |
| 2 | 169 ÷ 53 = 3 remainder 10 |
| 3 | 53 ÷ 10 = 5 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 57 | 114 |
| 168 and 123 | 6888 |
| 150 and 87 | 4350 |
| 18 and 184 | 1656 |
| 197 and 79 | 15563 |