Question

difference of two consecutive multiple of 3​

Answer 1

Answer:

Hope it helps you

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Answer 2

Answer:

All the answers given before this answer are correct. Though, I would like to add some more explanation so that it becomes easier to understand.

Two consecutive multiples of 3 can be written as 3k and 3k+3 where k is an integer. Clearly, 3 is a common factor of these two numbers , which means that HCF, being the highest common factor, is at least 3 i.e.

HCF(3k,3k+3)>=3……….(1)

Theorem: HCF of two positive integers a and b can be written as ma+nb where m and n are some integers. Further, if we create a set A(a,b) of all the values of ma+nb, then the least positive element of A(a,b) is equal to HCF(a,b).

Note: Proof of above theorem can be found in any number th...