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HCF AND LCM
1) The H.C.F. of 2² × 3³ × 5⁵, 2³ × 3² × 5² × 7 and 2⁴ × 3⁴ × 5 × 7² × 11 is
Correct Answer: 2² × 3² × 5
H.C.F. is the product of the lowest powers of common prime factors.
2) The L.C.M. of 2³ × 3² × 5 × 11, 2⁴ × 3⁴ × 5² × 7 and 2⁵ × 3³ × 5³ × 7² × 11 is
Correct Answer: 2⁵ × 3⁴ × 5³ × 7² × 11
L.C.M. is the product of the highest powers of all prime factors.
3) The H.C.F. of 12/25, 18/35, 21/40 and 9/10 is
Correct Answer: 3/1400
H.C.F. = H.C.F. of numerators / L.C.M. of denominators = 3 / 1400.
4) The L.C.M. of 2/3, 3/5, 4/7 and 9/13 is
Correct Answer: 36
L.C.M. of numerators = 36 and H.C.F. of denominators = 1.
5) The H.C.F. of 1.75, 5.6 and 7 is
Correct Answer: 0.35
Removing decimals gives 175, 560, 700 whose H.C.F. is 35 → 0.35.
6) The sum of two numbers is 528 and their H.C.F. is 33. How many such pairs are possible?
Correct Answer: 4
Let numbers be 33a and 33b ⇒ a + b = 16. Valid co-prime pairs = 4.
7) The product of two numbers is 4107 and their H.C.F. is 37. The greater number is
Correct Answer: 111
Numbers are 37 × 1 and 37 × 3 → greater number = 111.
8) Minimum number of rows to plant 21 mango, 42 apple and 56 orange trees
Correct Answer: 17
H.C.F. of 21, 42, 56 = 7 → Total rows = 119 ÷ 7 = 17.
9) The greatest length to measure exactly 7 m, 3 m 85 cm and 12 m 95 cm is
Correct Answer: 35 cm
H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.
10) The L.C.M. of 3, 2.7 and 0.09 is
Correct Answer: 27
L.C.M. of 300, 270 and 9 = 2700 → answer = 27.
