Least Common Multiple (LCM) of 74 and 169
The least common multiple (LCM) of 74 and 169 is 12506.
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 74 and 169?
First, calculate the GCD of 74 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 169 = 0 remainder 74 |
| 2 | 169 ÷ 74 = 2 remainder 21 |
| 3 | 74 ÷ 21 = 3 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 114 | 12198 |
| 93 and 102 | 3162 |
| 126 and 154 | 1386 |
| 170 and 150 | 2550 |
| 69 and 144 | 3312 |