1. Find the greatest weight which can be contained exactly in 80 kg & 100 kg.
Sol:
required weight = HCF(80, 100)
= 20 kg Answer
2. Find the LCM of 120, 162 and 198.
Sol:
∴ LCM = 2 × 2 × 2 × 3 × 3 × 3 × 3 ×5 × 11
= 35460 Answer
3. Find LCM of 2.4, 0.36 and 7.2.
Sol:
To calculate the LCM of decimal integers, make the decimal integers into whole numbers multiplying with any friendly numbers i.e. 10, 100, 1000, ……….. etc.
Now find out LCM of these whole numbers.
Finally divide this LCM by that friendly number which we used earlier.
∴ LCM = 2⁴ × 3² × 5 = 720
∴ required LCM = \(\frac{{720}}{{100}}\) = 7.2 Answer
4. Find LCM of \(\frac{8}{{15}},\frac{3}{{10}},\frac{9}{{40}}\).
Sol:
= \(\frac{{LCM\;of(8,3,9)}}{{HCF\;of(15,10,40)}}\)
= \(\frac{{72}}{5}\) Answer
5. Find HCF of \(\frac{8}{{15}},\frac{3}{{10}},\frac{9}{{40}}\).
Sol:
= \(\frac{{HCFof(8,3,9)}}{{LCMof(15,10,40)}}\)
= \(\frac{1}{{120}}\) Answer
6. The LCM of two numbers is 1280, their HCF is 25 and one of the number is 80. Find the other number.
Sol:
Product of numbers = LCM × HCF
x × 80 = 1280 × 25
x = 400 Answer
7. The HCF of two numbers is 42 and their LCM is 2646. Find the numbers if sum of the numbers is 672.
Sol:
Let numbers are 42x & 42y where x & y are co-prime.
∴ 42xy = 2646
xy = 63 ⟶ 3 × 3× 7
possible pairs of (x, y) are:
(1, 63)❌ ⟶ Numbers sum not 672
(3, 21)❌ ⟶ Not co-prime
(9, 7)✅ ⟶ Numbers sum = 42(9 + 7)
= 672
∴ Numbers are:
42x = 42 × 9 = 378
42 y = 42 × 7 = 294 Answer
8. The LCM of two numbers is 15 times their HCF. The sum of their LCM & HCF is 800. If one of the number is 150 then find the other number.
Sol:
LCM = 15HCF
LCM + HCF = 800
15HCF + HCF = 800
HCF = 50
∴ LCM = 15 × 50 = 750
∴ 50 × 750 = 150 × x
x = 250 Answer
9. Two numbers have 18 as their HCF and 153 as their LCM. Then how many pairs of such numbers are possible ?
Sol:
Numbers are 18x & 18y where x & y are co-prime
∴ 18xy = 153
xy = 8.5 ⟵ Not a whole Number
So No such pair is possible Answer
10. Find the LCM of 48, 168, 324 and 1400.
Sol:
Method(1):
∴ LCM = 2⁴ × 3⁴ × 5² × 7 = 226800 Answer
Method(2):
Method(3):
∴ LCM = 2⁴ × 3⁴ × 5² × 7 = 226800 Answer