Least Common Multiple (LCM) of 169 and 35
The least common multiple (LCM) of 169 and 35 is 5915.
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 35?
First, calculate the GCD of 169 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 35 = 4 remainder 29 |
| 2 | 35 ÷ 29 = 1 remainder 6 |
| 3 | 29 ÷ 6 = 4 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 40 | 3960 |
| 170 and 11 | 1870 |
| 136 and 117 | 15912 |
| 134 and 189 | 25326 |
| 100 and 137 | 13700 |