Question

find the smallest number which when divided by 8 9 10 15 20 give remainder 5​

Answer 1

365 is the smallest number which when divided by 8, 9, 10, 15, 20 gives a remainder of 5 every time.

Answer 2

Question

Find the smallest number which when divided by 8 9 10 15 20 give remainder 5.​

Answer

Step 1: Find the LCM of 8, 9, 10, 15, 20.

$\begin{array}{r | l} 2 &8,9,10,15,20 \\ \cline{2-2} 2 & 4,9,5,15,10 \\\cline{2-2} 2 & 2,9,5,15,5 \\ \cline{2-2} 3 & 1,9,5,15,5\\ \cline{2-2} 3 & 1,3,5,5,5\\ \cline{2-2} 5&1,1,5,5,5 \\\cline{2-2} & 1,1,1,1,1 \\ \end{array}$

The LCM of 8, 9, 10, 15 and 20 is ⇒ 2×2×2×3×3×5 = 360

Step 2: Add 5 to 360.

360+5 = 365

∴365 is the smallest number which is divided by 8, 9, 10, 15 and 20 and gives the remainder 5.

Additional Information

What is LCM?

Th least common multiple between any two or more numbers is known to be the LCM of those numbers. LCM is the acronym for Least Common Multiple.

What is Common Multiple?

The same multiples between 2 or more numbers is known to be the common multiple of those numbers.

What is HCF?

The highest common multiple between any two or more numbers is known to be the HCF of those numbers. HCF is the acronym for Highest Common Multiple.