Suppose mathrm‌p and mathrm‌q are the LCM and HCF respectively of two positive numbers. If mathrm‌p:mathrm‌q=14:1 and mathrm‌pq=1134, then what is the difference between the two numbers?
Given: p and q are the LCM and HCF of two positive numbers p:q=14:1,p⋅q=1134 Formula Used: LCM×HCF= Product of numbers Calculation: Let the value of p and q be 14x and x respectively According to the question pq=1134 ⇒(14x)(x)=1134 ⇒14x2=1134 ⇒x2=81 ⇒x=9 So, p=14×9=126 And q=1×9=9 Since p and q are the LCM&HCF of two numbers Then We can let two numbers are 9m and 9n [ since 9 is the HCF of two numbers] Now, According to the formula LCM×HCF= Product of numbers ⇒126×9=9m×9n ⇒mn=14 So, The possible value of m and n is (14,1)&(7,2) Case I: When we take m=14 and n=1, we get Numbers are 9×14=126 and 9×1=9 So, Difference between the number is 126−9=117 But we won't take this as it is not available in the options. Case II: If we take m=7 and n=2, we get Numbers are 9×7=63 and 9×2=18 So, Difference between the number is 63−18=45 ∴ The required difference is 45 .