Question

Express the hcf/lcm of 48 and 18 as a linear combination

Answer 1

18x + 48y = 6, where x = 3, y = –1

Solution:

Given numbers are 48 and 18.

Write it using linear combination, a = bq + r, where 0 ≤ r < b

   48 = 18 × 2 + 12

⇒ 18 = 12 × 1 + 6 (write 18 using the previous remainder 12)

⇒ 12 = 6 × 2 + 0 (write 12 using the previous remainder 6)

Remainder is zero. So, the process stops.

∴ HCF(18, 48) = 6

Now, Express 6 using 18 and 48.

6 = 18 – 12 × 1

6 = 18 – (48 – 18 × 2)

6 = 18 – 48 + 18 × 2

6 = 18 × 3 – 48 × 1

6 = 18 × 3 + 48 × (–1)

6 = 18x + 48y

18x + 48y = 6, where x = 3, y = –1

Hence 18x + 48y = 6 as the linear combination.