LCM and HCF
- There are five hobby clubs in a college viz. photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meets on the same day within 180 days?
-
View Hint View Answer Discuss in Forum
Gardening group meets once in 2 days, electronics group meets once in 3 days, chess group meets once in 4 days, yachting group meets once in 5 days and the photography group meets once in 6 days.
If they meet on the same day at one time, then the next time they will meet on same day again will be the LCM of 2, 3, 4, 5 and 6 which is equal to 60.Correct Option: A
Gardening group meets once in 2 days, electronics group meets once in 3 days, chess group meets once in 4 days, yachting group meets once in 5 days and the photography group meets once in 6 days.
If they meet on the same day at one time, then the next time they will meet on same day again will be the LCM of 2, 3, 4, 5 and 6 which is equal to 60.
Hence, within 180 days all the five groups will meet on the same day = 180/60 = 3 times.
- A, B and C start at the same time in the same direction to run around in 252s, B in 308s and C in 198s, all starting at the same point. After what time will they meet again at the starting point ?
-
View Hint View Answer Discuss in Forum
The time at which all the three persons meet will be the LCM of the time taken by each person individually to complete one round.
Correct Option: D
The time at which all the three persons meet will be the LCM of the time taken by each person individually to complete one round.
252 = 22 x 71 x 91
308 = 22 x 71 x 111
198 = 21 x 91 x 111
∴ LCM of 252, 308 and 198 = 22 x 71 x 91 x 111 = 2772
So, A, B and C will again meet at the starting point in 2772s i.e., 46 min and 12s
- What is the LCM of (x2 - y2 - z2 - 2yz), (x2 - y2 + z2 + 2xz) and (x2 + y2 - z2 - 2xy) ?
-
View Hint View Answer Discuss in Forum
x2 - y2 - z2 - 2yz = x2 - (y + z)2 = (x+ y + z)(x - y - z)
x2 - y2 + z2 + 2yz = (x + z)2 - y2 = (x + y + z) (x + y - z)
x2 + y2 - z2 - 2xy = (x - y)2 - z2 = (x - y + z) (x - y - z)Correct Option: B
x2 - y2 - z2 - 2yz = x2 - (y + z)2 = (x+ y + z)(x - y - z)
x2 - y2 + z2 + 2yz = (x + z)2 - y2 = (x + y + z) (x + y - z)
x2 + y2 - z2 - 2xy = (x - y)2 - z2 = (x - y + z) (x - y - z)
∴ LCM = (x + y + z) (x - y - z) (x - y + z)
- A man has four copper rods whose lengths are 52 m, 65 m, 78 m, 91 m, respectively. This man wants to cut pieces of same length from each of four rods. what is the least number of total pieces if he is to cut without any wastage ?
-
View Hint View Answer Discuss in Forum
The pieces cut from four rods is least, so length of the pieces is the HCF of 52, 65, 78 and 91 which is 13.
Correct Option: C
The pieces cut from four rods is least, so length of the pieces is the HCF of 52, 65, 78 and 91 which is 13.
∴ Number of pieces cut =(52 + 65 + 78 + 91)/13 = 22
- A, B, and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252s, B in 308s and C in 198s, all starting of the same point. After what time will they meet again at the string point ?
-
View Hint View Answer Discuss in Forum
The time which all the three persons meet will be the LCM of the time by each person individually to complete one round.
252 = 22 x 71 x 91
308 = 22 x 71 x 111
198 = 21 x 91 x 111
Correct Option: D
The time which all the three persons meet will be the LCM of the time by each person individually to complete one round.
252 = 22 x 71 x 91
308 = 22 x 71 x 111
198 = 21 x 91 x 111
∴ LCM of 252, 308 and 198 = 22 x 71 x 91 x 111 = 2772
So,A,B and C will again meet at the starting point in 2772 i.e.,46 min and 12s.
