If two positive integers x and y are expressible in terms of primes as x = p2q3 and y = p3q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain.
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Find the LCM and HCF of the following pairs of integer and verify that LCM×HCF=Product of the two numbers.
Solution : i) 26 and 91 26=2×13×1(expressing as product of it’s prime factors) 91=7×13×1(expressing as product of it’s prime factors) So, LCM(26,91)=2×7×13×1=182 HCF(26,91)=13×1=13 Verification: LCM×HCF=13×182=2366 Product of 26 and 91 =2366 Therefore,LCM×HCF=Product of the two numbers . i) 510 and...
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Find the LCM and HCF of the following integers by applying the prime factorization method. i) 12,15 and 21 ii) 17,23 and 29 iii) 8,9 and 25
Solution : i) 12,15 and 21 12=2×2×3 15=5×3 21=7×3 From the above ,HCF(12,15,21)=3and LCM(12,15,21)=420 ii)17,23,and 29 17=17×1 23=23×1 29=29×1 From the above ,HCF(17,23,29)=1and LCM(17,23,29)=11339 iii)8,9 and 25 8=2×2×2 9=3×3 25=5×5 From the above ,HCF(8,9,25)=1and LCM(8,9,25)=1800
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State Fundamental theorem of arithmetic. Is it possible for the HCF and LCM of two numbers to be 18 and 378 respectively. Justify your answer.
Solution: Every composite number can be expressed (factorised) as a product of primes and this factorisation is unique, apart from the order in which the prime factors occur. Yes. Justification: HCF...
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The HCF of 65 and 117 is expressible in the form 65m - 117. Find the value of m. Also find the LCM of 65 and 117 using prime factorization method.
Solution: 117 = 65 x 1 + 52 65 = 52 x 1 + 13 65 = 13 x 5 + 0 => HCF(65, 117) = 13 Since, HCF(65, 117) = 65m - 117 => 13 = 65m - 117 => 65m...
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If two positive integers a and b are written as a = x^3y^2 and b = xy^3; x, y are prime numbers, then HCF (a, b) is
Correct answer is (B) xy2
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If the HCF of 55 and 99 is expressible in the form 55m - 99, then the value of m is (A) 4 (B) 2 (C) 1 (D) 3
Correct answer is (B) 2
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Define HOE of two positive integers and find the HCF of the following pairs of numbers: (i) 32 and 54 (ii) 18 and 24 (iii) 70 and 30 (iv) 56 and 88
By applying Euclid’s division lemma (i) 54 = 32 × 1 + 22 Since remainder ≠ 0, apply division lemma on division of 32 and remainder 22. 32 = 22 × 1 +...
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If the HCF of 408 and 1032 is expressible in the form 1032m − 408 × 5, find m.
General integers are 408 and 1032 where 408 < 1032 By applying Euclid’s division lemma, we get 1032 = 408 × 2 + 216 Since remainder ≠ 0, apply division lemma on division...
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If the HCF of 657 and 963 is expressible in the form 657x + 963x − 15, find x.
657 and 963 By applying Euclid’s division lemma 963 = 657 × 1 + 306 Since remainder ≠ 0, apply division lemma on division 657 and remainder 306 657 = 306 × 2 +...
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Two positive integers p and q can be expressed as = ab^2 and q =a^2b, a and b are prime numbers. what is the LCM Of p and q ?
The correct answer is a2 b2
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