Let d be the HCF of 24 and 36. Find two numbers a and b Such that d=24a+36b.

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Solution

Applying Euclid's Division Lemma to 24 and 36, we get
36 = 241 + 12 ...(1)
24 = 212 + 0
Thus, the HCF of 24 and 36 is 12.
From (1), we have,
⇒ 12 = 36 - 24
⇒ 12 = 24(-1) + 36(1)
⇒ 12 = 24a + 36b
Where a = -1 and b = 1

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