Question

41. Which number is a multiple of all the three numbers 4, 8 and 6 ?​

Answer 1

2 is the number which has these three numbers as multiples as 2 is the even number

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Answer 2

Given :- Which number is a multiple of all the three numbers 4, 8 and 6 ?

Solution :-

Since LCM is a multiple of all three numbers, finding LCM by prime factorization method we get,

prime factors of 4 , 8 and 6 are :-

→ 4 = 2 * 2 = 2²

→ 8 = 2 * 2 * 2 = 2³

→ 6 = 2¹ * 3¹

so,

→ LCM = Product of highest power of all the factors = 2³ * 3¹ = 2 * 2 * 2 * 3 = 24

therefore, 24 is the smallest number which is multiple of all three given numbers .

Now, all multiple of 24 will also be the multiple of 4, 8 and 6 .

Extra knowledge :-

• HCF(Highest common factor) = Greatest number which exactly divides all the given numbers .
• HCF = Product of least power of common factors .

Learn more :-

what is the largest number which divides 270 and 426, leaves a remainder of 6 in each case

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