18. The product of two numbers is 2560 and their LCM is 320. Find their HCF.
19. The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 7
the other.
20. The HCF and LCM of two numbers are 131 and 8253 respectively. If one of the nu
Answers
Answer:
18.There's an identity
Product of two numbers = LCM * HCF
By substituting given values in identity
We get,
2560 = 320*HCF
HCF = 2560/320
HCF = 8
Therefore HCF of the two numbers is 8
19. LET THE NO BE A AND B
hcf * lcm = a*b
145*2175=725*b
b=145*2175 divided by725
b=435
20. The HCF and LCM of two numbers is 131 and 8253, respectively. If one number is 917, can you find the other?
Let us see an example.
Consider two numbers 27 and 36. Let us factorize them,
27 = 3 x3 x3
36 = 2 x2 x3 x3
HCF of 27 and 36 = 9, and LCM = 2x2x3x3x3 = 108.
Multiply LCM and HCF: 9x108 = 972.
Next multiply the two numbers: 27x36 = 972.
So the product of the two numbers is the same as the product of their HCF and LCM.
Following the same principle in the current problem: HCF x LCM = 131x8253 = 1081143
So if one number is 917, the other number is 1081143/917 = 1179.
Check: 917 = 7x131
1179 = 131x9.
HCF = 131, and LCM = 7x9x131 = 8253. Correct.
The other number is 1179.
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