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Q: A Former plants three different types of plants in equal number in a garden. All plants of one type are planted to form a rectangle, in which no rectangel contains more than one type no plants of any type are left out. After all the plants were planted, the rectangle of plant A had 70 rows, the rectange of plant B had 28 rows and the rectange of plant C had 42 rows. Find the mininum number of plants of each type planted by the farmer in the garden.
  • A. 70
  • B. 420
  • C. 210
  • D. 140
Correct Answer: Option B - Minimum number of plants of each type planted by the farmer = LCM of 70, 28, and 42 70 = 2 × 5 × 7 28 = 2 × 2 × 7 42 = 2 × 3 × 7 LCM • 2 × 2 × 3 × 5 × 7 = 420 Hence the Minimum number of plants = 420
B. Minimum number of plants of each type planted by the farmer = LCM of 70, 28, and 42 70 = 2 × 5 × 7 28 = 2 × 2 × 7 42 = 2 × 3 × 7 LCM • 2 × 2 × 3 × 5 × 7 = 420 Hence the Minimum number of plants = 420

Explanations:

Minimum number of plants of each type planted by the farmer = LCM of 70, 28, and 42 70 = 2 × 5 × 7 28 = 2 × 2 × 7 42 = 2 × 3 × 7 LCM • 2 × 2 × 3 × 5 × 7 = 420 Hence the Minimum number of plants = 420