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 : 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...

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

Solution : We know, HCF×LCM=Product of two numbers i.e 9×LCM=306×657 LCM=306×657/9=22338

Solution: Since, 2520 = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 23 x 32 x 5 x 7 Therefore,  p = 2 and q = 5

Solution: LCM x HCF = Product of two numbers => LCM x 18 = 306 x 1314 => LCM = (306 x 1314)/18 = 22338

Solution: x = p2q3 and y = p3q HCF(x, y) = p2 x q LCM(x, y) = p3 x q3 LCM(x, y) = (p x q2) x HCF(x, y) => LCM is a multiple of HCF.

Correct answer is (B) 2

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...

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 +...

The correct answer is 6p