Entrance Exams
Govt. Exams
Numbers are 10, 15, 20. 10 = 2 × 5, 15 = 3 × 5, 20 = 2² × 5. LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60 × 10 = 600.
HCF × LCM = Product of numbers. 36 × LCM = 408 × 468. LCM = (408 × 468) ÷ 36 = 190944 ÷ 36 = 5304.
12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 8 × 9 = 72.
Let numbers be 3k and 5k.
Their HCF is k = 8.
So numbers are 3(8) = 24 and 5(8) = 40.
72 = 2³ × 3², 90 = 2 × 3² × 5.
Common factors: 2 and 3². HCF = 2 × 3² = 2 × 9 = 18.
LCM(12, 18) = 36.
Time for both = 36/(36/12 + 36/18) = 36/(3 + 2) = 36/5 = 7.2 minutes.
150 = 2 × 3 × 5², 200 = 2³ × 5².
Common factors: 2 and 5². HCF = 2 × 5² = 2 × 25 = 50.
HCF × LCM = Product of numbers. 12 × 144 = 36 × other. 1728 = 36 × other.
Other = 1728 ÷ 36 = 48.
20 = 2² × 5, 30 = 2 × 3 × 5, 40 = 2³ × 5. LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120.
45 = 3² × 5, 60 = 2² × 3 × 5, 75 = 3 × 5².
Common factors: 3 and 5. HCF = 3 × 5 = 15.