HCF and LCM Examples 1

In this class, We discuss HCF and LCM Examples 1.

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Example 1:

Find the greatest number by dividing 1657 and 2037, and leave the remainder 6 and 5, respectively.

Solution:

The greatest number, which divides 1657, should leave the remainder 6.

Similarly, divide the number 2037 and leave remainder 5.

We need to find GCD or HCF.

1657 – 6 = 1651

2037 – 5 = 2032

HCF(1651, 2032) is the greatest number that divides exactly.

The same HCF will leave the remainder 6 and 5 for the numbers 1657 and 2037.

HCF(1651, 2032) = 127

Example 2:

Find the least number divided by 6, 7, 8, 9, and 12, leaving the same remainder 1.

Solution:

They ask to find the least number divided by 6, 7, 8, 9, and 12.

We need to identify the LCM.

The below diagram shows the LCM of 6, 7, 8, 9, and 12.

LCM = 504

Add 1 to LCM = 505

Five hundred five will leave the remainder 1 when divided by 6, 7, 8, 9, and 12.

Example 3:

Find the least number, divisible by 5, 6, 7, and 8 leaves a remainder of 3. but when divided by nine leaves a remainder of zero.

Solution:

LCM(5, 6, 7, 8) = 840

840 is the least number divisible by 5, 6, 7, and 8.

840 * x + 3, we can place different values in place of x.

840 * 1 + 3 will leave the remainder 3 when divisible by 5, 6, 7, and 8.

840 * 2 + 3, another number divisible by 5, 6, 7, and 8 leaves the remainder of 3.

Find the least value of x for which 840 * x + 3 is divisible by 9.

x= 2