2. Find L.C.M. of the following numbers:
(a) 20,50
(b) 72,96
(d) 4,8,12
(e) 6,15,25,30
(g) 10,15,20,25
(h) 16,18,32,48
(c) 55,77
(f) 12,18,24,36
(i) 12,15,18,24
Answers
Answer:
a). 2*5*2*5=100
b). 2*2*2*3*3*4=288
d). 2*2*2*3=24
e). 2*3*5*5=150
g).2*5*3*2*5=300
h).2*2*2*2*3*3*2=288
c).11*5*7=385
f).2*2*3*3*2=72
I).2*2*3*5*3*2=360
Step-by-step explanation:
- LCM(20,50) = (20 × 50) / GCF(20,50)
= (20 × 50) / 10
= 1000 / 10
= 100
Therefore,
LCM(20, 50) = 100
2. LCM(72,96) = (72 × 96) / GCF(72,96)
= (72 × 96) / 24
= 6912 / 24
= 288
Therefore,
LCM(72, 96) = 288
3LCM(4, 8, 12) =
LCM(LCM(4, 8), 12)
Working from the innermost parentheses outward:
LCM(4,8) = (4 × 8) / GCF(4,8)
= (4 × 8) / 4
= 32 / 4
= 8
LCM(8,12) = (8 × 12) / GCF(8,12)
= (8 × 12) / 4
= 96 / 4
= 24
Therefore,
LCM(4, 8, 12) = 24
4.LCM(6, 15, 25, 30) =
LCM(LCM(LCM(6, 15), 25), 30)
Working from the innermost parentheses outward:
LCM(6,15) = (6 × 15) / GCF(6,15)
= (6 × 15) / 3
= 90 / 3
= 30
LCM(30,25) = (30 × 25) / GCF(30,25)
= (30 × 25) / 5
= 750 / 5
= 150
LCM(150,30) = (150 × 30) / GCF(150,30)
= (150 × 30) / 30
= 4500 / 30
= 150
Therefore,
LCM(6, 15, 25, 30) = 150
5.LCM(10, 15, 20, 25) =
LCM(LCM(LCM(10, 15), 20), 25)
Working from the innermost parentheses outward:
LCM(10,15) = (10 × 15) / GCF(10,15)
= (10 × 15) / 5
= 150 / 5
= 30
LCM(30,20) = (30 × 20) / GCF(30,20)
= (30 × 20) / 10
= 600 / 10
= 60
LCM(60,25) = (60 × 25) / GCF(60,25)
= (60 × 25) / 5
= 1500 / 5
= 300
Therefore,
LCM(10, 15, 20, 25) = 300
6.LCM(16, 18, 32, 48) =
LCM(LCM(LCM(16, 18), 32), 48)
Working from the innermost parentheses outward:
LCM(16,18) = (16 × 18) / GCF(16,18)
= (16 × 18) / 2
= 288 / 2
= 144
LCM(144,32) = (144 × 32) / GCF(144,32)
= (144 × 32) / 16
= 4608 / 16
= 288
LCM(288,48) = (288 × 48) / GCF(288,48)
= (288 × 48) / 48
= 13824 / 48
= 288
Therefore,
LCM(16, 18, 32, 48) = 288
7. LCM(55,77) = (55 × 77) / GCF(55,77)
= (55 × 77) / 11
= 4235 / 11
= 385
Therefore,
LCM(55, 77) = 385
8.LCM(12, 18, 24, 36) =
LCM(LCM(LCM(12, 18), 24), 36)
Working from the innermost parentheses outward:
LCM(12,18) = (12 × 18) / GCF(12,18)
= (12 × 18) / 6
= 216 / 6
= 36
LCM(36,24) = (36 × 24) / GCF(36,24)
= (36 × 24) / 12
= 864 / 12
= 72
LCM(72,36) = (72 × 36) / GCF(72,36)
= (72 × 36) / 36
= 2592 / 36
= 72
Therefore,
LCM(12, 18, 24, 36) = 72
9.LCM(12, 15, 18, 24) =
LCM(LCM(LCM(12, 15), 18), 24)
Working from the innermost parentheses outward:
LCM(12,15) = (12 × 15) / GCF(12,15)
= (12 × 15) / 3
= 180 / 3
= 60
LCM(60,18) = (60 × 18) / GCF(60,18)
= (60 × 18) / 6
= 1080 / 6
= 180
LCM(180,24) = (180 × 24) / GCF(180,24)
= (180 × 24) / 12
= 4320 / 12
= 360
Therefore,
LCM(12, 15, 18, 24) = 360