Least Common Multiple (LCM) of 169 and 77
The least common multiple (LCM) of 169 and 77 is 13013.
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 169 and 77?
First, calculate the GCD of 169 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 77 = 2 remainder 15 |
| 2 | 77 ÷ 15 = 5 remainder 2 |
| 3 | 15 ÷ 2 = 7 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 115 | 20010 |
| 83 and 54 | 4482 |
| 196 and 138 | 13524 |
| 145 and 174 | 870 |
| 42 and 177 | 2478 |