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Answers
Answer:
5.960
6.We know that in order to find the time when the three lights will change simultaneously again after 7 a.m., we need to find the LCM of 48, 72, and 108. Hence, after converting 432 seconds into minutes and seconds, we get: 432 seconds = 7 minutes and 12 seconds.
8.Amount of diesel present in the first tank = 403 litres
Amount of diesel present in the second tank = 434 litres
Amount of diesel present in the third tank = 465 litres
To measure the three tankers, we need to find the container’s maximum measuring capacity. We need to find the HCF because the measuring capacity is smaller than 403 litres, 434 litres and 465 litres.
The Highest Common Factor or HCF is the largest common divisor or gcd of two or more positive integers, as the mathematics rules dictate, appears to be the largest positive integer that divides the numbers without leaving a remainder.
The maximum capacity of container = H.C.F. of (403, 434, 465)
Let us find the prime factorization of 403, 434 and 465.
⇒ Factors of 403 = 13 x 31
⇒ Factors of 434 = 2 x 7 x 31
⇒ Factors of 465 = 3 x 5 x 31
∴ H.C.F of (403, 434, 465) = 31
Therefore, 31 litres of the container is required to measure the quantity. i. e. The maximum measuring capacity is 31 litres
9.95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.
10..1152
10.LCM (The Least Common Multiple) of any two is the value that is evenly divisible by the two given numbers.
(a) 9 and 4
9 =3 × 3
4 = 2 × 2
L.C.M of 9 and 4 = 2×2×3×3 = 36
(b) 12 and 5
12 = 2 x 2 x 3
5 = 5 x 1
L.C.M of 12 and 5 = 2×2×3×5 = 60
(c) 6 and 5
6 = 2 × 3
5 = 5× 1
L.C.M of 6 and 5 = 2 × 3 × 5 = 30
(d) 15 and 4
15 = 3× 5
4 = 2 × 2
L.C.M of 15 and 4 = 2 × 2 × 3 × 5 = 60
Yes, the L.C.M. is equal to the product of two numbers in each case. And L.C.M. is also the multiple of 3
11.(a) L.C.M of 5 and 20
= 2 – 2 – 5 = 20
(b) L.C.M of 6 and 18
= 2 – 3 – 3 = 18
(c) L.C.M of 12 and 48
= 2 – 2 – 2 – 2 – 3 = 48
(d) L.C.M of 9 and 45
= 3 – 3 – 5 = 45