Can two numbers have 15 as HCF and 350 as LCM? WHY? MAKE IT BY PROCESS
Answers
Answered by
128
HCF - Highest Common Factor
For two numbers, their HCF is the largest number which divides both.
LCM - Least Common Multiple
For two numbers, their LCM is the smallest number which is a multiple both.
Now, HCF divides both numbers. And both numbers perfectly divide LCM.
So, HCF must perfectly divide. LCM.
In other words, for LCM÷HCF, remainder must be zero.
Here, LCM = 350
And, HCF = 15
Clearly, 350/15 = 23.33 (remainder not zero)
Thus, there do not exist two numbers whose HCF is 15 and LCM is 350
For two numbers, their HCF is the largest number which divides both.
LCM - Least Common Multiple
For two numbers, their LCM is the smallest number which is a multiple both.
Now, HCF divides both numbers. And both numbers perfectly divide LCM.
So, HCF must perfectly divide. LCM.
In other words, for LCM÷HCF, remainder must be zero.
Here, LCM = 350
And, HCF = 15
Clearly, 350/15 = 23.33 (remainder not zero)
Thus, there do not exist two numbers whose HCF is 15 and LCM is 350
Answered by
43
Answer:
Step-by-step explanation:
No ,2 numbers cannot have HCF as 15 and LCM as 350 .
Because LCM>HCF and HCF of 2 numbers should divide the LCM completely.
Here , the 1st criteria is fulfilled but the 2nd criteria is not.
Since 350/15=70/3= 23 1/3 ∉ N.
350 is not completely divisible by 15.
Hence
2 numbers cannot have HCF as 15 and LCM as 350
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