Question

Use euclid's algorithm to find the H C.F and L.C.M of 550 and 882

Answer 1

Solution:

If , a , b  are any two integers,then there exist positive integers, p and q such that,  By applying Euclid division Algorithm

 a= b p + q, where, 0 ≤ q < b.

Now, we will use this Algorithm to find HCF of 550 and 882.

882= 550 × 1 +332

550= 332×1+218

332=218×1+114

218=114×1+104

114=104×1+10

104=10×10 +4

10=4×2+2

4=2×2+0

H C F of 550 and 882= 2

Also,⇒ (H C F × L CM) of two numbers= Product of two numbers

  ⇒ 2 × L C M of two numbers = 550 × 882

⇒ L C M of two numbers

                $=\frac{550 \times 882}{2}\\\\=\frac{485100}{2}\\\\=242550$