Question

LCM and HCF of 183 and 64​

Answer 1

Answer:

HCF=1

LCM=4096

Step-by-step explanation:

HCF:

Answer:

GCF = 1

for the values 64, 183

Solution by Factorisation:

The factors of 64 are: 1, 2, 4, 8, 16, 32, 64

The factors of 183 are: 1, 3, 61, 183

Then the greatest common factor is 1.

The LCM of numbers is the smallest number that is divisible by all given numbers.

LCM:

Find the prime factorisation of each number.

183=3x61

64=$2^{6}$

Write numbers and prime factors in table-like format. The rows are numbers, and prime factors are the columns. Thus, each row is the prime factorisation of the corresponding number.

Fill empty spaces with ones.

In each column, find the largest factor.

Primes  2, 3, 61

Number 183 = 1x3x61

Number 64 = $2^{6}$x1x1

Largest factors = $2^{6}$, 3, 61

The product of the largest factors is the least common multiple: $2^{6}$⋅3⋅61=11712.

Thus, LCM(183,64)=11712.

Alternatively, the least common multiple can be found as the product of numbers divided by the greatest common divisor of the numbers: LCM(a,b)=axbxGCD(a,b).

Since GCD(183,64)=1

then LCM(183,64)=183x64xGCD(183,64)=117121=11712.

Answer: LCM(183,64)=11712.