Least Common Multiple (LCM) of 60 and 169
The least common multiple (LCM) of 60 and 169 is 10140.
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 60 and 169?
First, calculate the GCD of 60 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 169 = 0 remainder 60 |
| 2 | 169 ÷ 60 = 2 remainder 49 |
| 3 | 60 ÷ 49 = 1 remainder 11 |
| 4 | 49 ÷ 11 = 4 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 44 | 220 |
| 100 and 162 | 8100 |
| 132 and 134 | 8844 |
| 78 and 65 | 390 |
| 31 and 183 | 5673 |