Least Common Multiple (LCM) of 153 and 169
The least common multiple (LCM) of 153 and 169 is 25857.
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 153 and 169?
First, calculate the GCD of 153 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 169 = 0 remainder 153 |
| 2 | 169 ÷ 153 = 1 remainder 16 |
| 3 | 153 ÷ 16 = 9 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 56 | 11144 |
| 153 and 12 | 612 |
| 120 and 174 | 3480 |
| 106 and 77 | 8162 |
| 64 and 92 | 1472 |