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 |
|---|---|
| 42 and 140 | 420 |
| 174 and 125 | 21750 |
| 200 and 14 | 1400 |
| 32 and 101 | 3232 |
| 118 and 64 | 3776 |